The annual percentage yield (APY) is the actual percent a quantity increases in one year. It can be
calculated as
r k
APY = (1+ k ) − 1 (2.4.3)
This is equivalent to finding the value of $1 after 1 year, and subtracting the original dollar.
Example
Bank A offers an account paying 1.2% compounded quarterly. Bank B offers an account paying 1.1%
compounded monthly. Which is offering a better rate?
Solution
We can compare these rates using the annual percentage yield – the actual percent increase in a year.
Bank A: 0.012 4 = 1.2054%
APY =(1+ ) − 1 = 0.012054
Bank B: 0.011 12 = 1.1056%
APY =(1+ ) − 1 = 0.011056
Bank B’s monthly compounding is not enough to catch up with Bank A’s better APR. Bank A offers a
better rate.
A Limit to Compounding
As we saw earlier, the amount we earn increases as we increase the compounding frequency. The
table, though, shows that the increase from annual to semi-annual compounding is larger than the
increase from monthly to daily compounding. This might lead us to believe that although increasing
the frequency of compounding will increase our result, there is an upper limit to this process.
To see this, let us examine the value of $1 invested at 100% interest for 1 year.
Frequency Value
Annual $2
Quarterly $2.441406
Monthly $2.613035
Daily $2.714567
Hourly $2.718127
Once per minute $2.718279
Once per second $2.718282
These values do indeed appear to be approaching an upper limit. This value ends up being so
important that it gets represented by
its own letter, much like how represents a number.
Definition: Euler's number:
is the letter used to represent the value that 1 k approaches as gets big.
e (1 + ) k
Because is often used as the base of an exponential, most scientific and graphing calculators
have a button that can calculate
powers of , usually labeledx. Some computer software instead defines a function , where
exp(x) = x .
exp(x)
Because arises when the time between compounds becomes very small, allows us to define
continuous growth and allows us
e e
to define a new toolkit function, f(x) = ex .
2.4.9
Definition: Continuous Growth Formula
Continuous Growth can be calculated using the formula
f(x) = aerx
where
is the starting amount
is the continuous growth rate
This type of equation is commonly used when describing quantities that change more or less
continuously, like chemical reactions, growth of large populations, and radioactive decay.
Example
Radon-222 decays at a continuous rate of 17.3% per day. How much will 100mg of Radon-222 decay
to in 3 days? Solution
Since we are given a continuous decay rate, we use the continuous growth formula. Since the
substance is decaying, we know the growth rate will be negative: = -0.173
f(3) = 100 −0.173(3) ≈ 59.512 mg of Radon-222 will remain.
Exercise
Interpret the following: S(t) = 20 0.12t if S(t) represents the growth of a substance in grams, and time
is measured in days.
Answer
An initial substance weighing 20g is growing at a continuous rate of 12% per day.
Continuous growth is also often applied to compound interest, allowing us to talk about continuous
compounding.
Example
If $1000 is invested in an account earning 10% compounded continuously, find the value after 1 year.
Solution
Here, the continuous growth rate is 10%, so = 0.10. We start with $1000, so = 1000.
To find the value after 1 year,
f(1) = 1000e0.10(1) ≈ $1105.17
Notice this is a $105.17 increase for the year. As a percent increase, this is 105.17 increase
over the
original $1000. 1000 = 0.10517 = 10.517%
Notice that this value is slightly larger than the amount generated by daily compounding in the table
computed earlier.
The continuous growth rate is like the nominal growth rate (or APR) – it This is different than the
annual growth rate used in the formula
f(x) =
reflects the actual amount the output grows in a year.
reflects the growth rate before compounding takes effect. a(1 + r)x , which is like the annual
percentage yield – it
While the continuous growth rate in the example above was 10%, the actual annual yield was
10.517%. This means we could write two different looking but equivalent formulas for this account’s
growth:
f(t) = 1000 0.10t using the 10% continuous growth rate
f(t) = 1000(1.10517)t using the 10.517% actual annual yield rate.
Important Topics of this Section
Percent growth
Exponential functions
Finding formulas
Interpreting equations
Graphs
Exponential Growth & Decay
Compound interest
Annual Percent Yield
Continuous Growth
This page titled 2.4: Modeling with Exponential Functions is shared under a CC BY-SA 4.0 license
and was authored, remixed, and/or curated by David Lippman & Melonie Rasmussen (The
OpenTextBookStore) via source content that was edited to the style and standards of the LibreTexts
platform; a detailed edit history is available upon request.
4.1: Exponential Functions by David Lippman & Melonie Rasmussen is licensed CC BY-SA 4.0.
Original source:
2.4E: Exponential Functions (Exercises)
Section 4.1 Exercise
For each table below, could the table represent a function that is linear, exponential, or neither?
1. 2.
3. 4.
5. 6.
A population numbers 11,000 organisms initially and grows by 8.5% each year. Write an
exponential model for the population.
A population is currently 6,000 and has been increasing by 1.2% each day. Write an
exponential model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
MATHEMATICAL METHODS AND EQUATIONS
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
c. Below what the model predicts $5.70
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential
model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is
estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year
2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each
year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be
covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the
approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12%
each year. Find the residual value of the furniture 6 years after purchase.
Find a formula for an exponential function passing through the two points.
13.
(0, 6) , (3, 750)
14.
(0, 3) , (2, 75)
15.
(0, 2000) , (2, 20)
16.
(0, 9000) , (3, 72)
17.
(−1, ) , (3, 24)
18.
(−1, 5 ) , (1, 10)
19.
(−2, 6) , (3, 1)
20.
(−3, 4) , (3, 2)
21.
(3, 1) , (5, 4)
22.
(2, 5) , (6, 9)
A radioactive substance decays exponentially. A scientist begins with 100 milligrams of a
radioactive substance. After 35 hours, 50 mg of the substance remains. How many milligrams will
remain after 54 hours?
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a
radioactive substance. After 31 hours, 55 mg of the substance remains. How many milligrams will
remain after 42 hours?
A house was valued at $110,000 in the year 1985. The value appreciated to $145,000 by the
year 2005. What was the annual growth rate between 1985 and 2005? Assume that the house value
continues to grow by the same percentage. What did the value equal in the year 2010?
An investment was valued at $11,000 in the year 1995. The value appreciated to $14,000 by
the year 2008. What was the annual growth rate between 1995 and 2008? Assume that the value
continues to grow by the same percentage. What did the value equal in the year 2012?
A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2013?
A car was valued at $24,000 in the year 2006. The value depreciated to $20,000 by the year
2009. Assume that the car value continues to drop by the same percentage. What was the value in the
year 2014?
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the
amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and
continuously.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the
amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and
continuously.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
3% compounded quarterly.
Find the annual percentage yield (APY) for a savings account with annual percentage rate of
5% compounded monthly.
A population of bacteria is growing according to the equation P (t) = 1600 0.21 t, with t
measured in years. Estimate when the population will exceed 7569.
A population of bacteria is growing according to the equation P (t) = 1200 0.17 t, with t
measured in years. Estimate when the population will exceed 3443.
In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wage was $2.30
per hour. Assume the
minimum wage grows according to an exponential model , where t represents the time in years
after 1960. [UW]
a. Find a formula for . w(t)
w(t)
b. What does the model predict for the minimum wage in 1960?
c. If the minimum wage was $5.15 in 1996, is this above, below or equal to what the model predicts?
36. In 1989, research scientists published a model for predicting the cumulative
number of AIDS cases (in thousands) reported in the United States:
t − 1980 3 , where is the year. This paper was considered a
a (t) = 155( 10 ) t
“relief”, since there was a fear the correct model would be of exponential type. Pick
two data points predicted by the research model to construct a new exponential
model a(t)
for the number of cumulative AIDS cases. Discuss how the two models
b(t)
differ and explain the use of the word “relief.” [UW]
You have a chess board as pictured, with squares numbered 1 through 64. You also have a
huge change jar with an unlimited number of dimes. On the first square you place one dime. On the
second square you stack 2 dimes. Then you continue, always doubling the number from the previous
square. [UW]
How many dimes will you have stacked on the 10th square?
How many dimes will you have stacked on the nth square?
How many dimes will you have stacked on the 64th square?
Assuming a dime is 1 mm thick, how high will this last pile be?
The distance from the earth to the sun is approximately 150 million km. Relate the height of
the last pile of dimes to this distance.
Answer
1. Linear
3. Exponential
5. Neither
P (t) = 11, 000(1.085)t
47622 Fox
11. $17561.70
y =. 6(5)x
y = 2000(0.1)x
17. x
y = 3(2)
x
19. y = ( 1 − ( 1 = 2.93(0.699)x
6 ) 5 ) 5
6
21. y = (2)x
8
23. 34.32
mg
1.39%; $155,368.09
$4,813.55
Annual $7353.84 Quarterly $7,469.63 Monthly $7,496.71 Continuously $7,510.44
3.03%
7.4 years
35a. w(t) = (1.113)(1.046)t
b. $1.11
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4.1E: Exponential Functions (Exercises) by David Lippman & Melonie Rasmussen is licensed CC
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2.5: Compound Interest
2.4 Learning Objectives
Use the compound interest formula to compute beginning or ending balance in an account
With simple interest, we were assuming that we pocketed the interest when we received it. In a
standard bank account, any interest we earn is automatically added to our balance, and we earn
interest on that interest in future years. This reinvestment of interest is called compounding.
Suppose that we deposit $1000 in a bank account offering 3% interest, compounded monthly. How
will our money grow?
The 3% interest is an annual percentage rate (APR) – the total interest to be paid during the year.
Since interest is being paid
monthly, each month, we will earn 3% per month.
= 0.25%
In the first month,
= $1000
r = 0.0025(0.25%)
= $1000(0.0025) = $2.50
= $1000 +$2.50 = $1002.50
In the first month, we will earn $2.50 in interest, raising our account balance to $1002.50.
In the second month,
= $1002.50
(rounded)
= $1002.50(0.0025) = $2.51
= $1000 +$2.50 = $1002.50
Notice that in the second month we earned more interest than we did in the first month. This is
because we earned interest not only on the original $1000 we deposited, but we also earned interest on
the $2.50 of interest we earned the first month. This is the key advantage that compounding of interest
gives us.
Calculating out a few more months:
Starting balance Ending Balance
2 1002.502.51 1005.01
3 1005.012.51 1007.52
5 1010.042.53 1012.57
8 1017.642.54 1020.18
10 1022.732.56 1025.29
1025.292.56 1027.85
To find an equation to represent this, if
Pm
represents the amount of money after
m
months, then we could write the recursive
equation:
= $1000
m = (1 +0.0025) m−1
You probably recognize this as the recursive form of exponential growth. If not, we could go through
the steps to build an explicit equation for the growth:
P0 = $1000
1 = 1.0025 0 = 1.0025(1000)
P2 = 1.0025P1 = 1.0025(1.0025(1000)) = 1.00252(1000)
= 1.0025 2 = 1.0025 (1.00252(1000)) = 1.00253(1000)
= 1.0025 3 = 1.0025 (1.00253(1000)) = 1.00254(1000)
Observing a pattern, we could conclude
= (1.0025)m($1000)
Notice that the $1000 in the equation was , the starting amount. We found 1.0025 by adding
one to the growth rate divided by
0
12, since we were compounding 12 times per year.
Generalizing our result, we could write
m
A= 0(1+ )
In this formula:
is the number of compounding periods (months in our example)
is the annual interest rate
r
is the number of compounds per year.
While this formula works fine, it is more common to use a formula that involves the number of years,
rather than the number of
compounding periods. If is the number of years, then . Making this change gives us the standard
formula for compound interest.
Compound Interest
tn
A= 0(1+ )
is the balance in the account after N years.
is the starting balance of the account (also called initial deposit, or principal)
0
is the annual interest rate in decimal form
is the number of compounding periods in one year.
n
If the compounding is done annually (once a year),
.
If the compounding is done quarterly,
n = 4
.
If the compounding is done monthly,
.
If the compounding is done daily,
n = 365
.
The most important thing to remember about using this formula is that it assumes that we put money
in the account once and let it sit there earning interest.
Example 1
A certificate of deposit (CD) is a savings instrument that many banks offer. It usually gives a higher
interest rate, but you cannot access your investment for a specified length of time. Suppose you
deposit $3000 in a CD paying 6% interest, compounded monthly. How much will you have in the
account after 20 years?
Solution
In this example,
P0 = $3000
the initial deposit
r = 0.06 6% annual rate
12 months in 1 year
t = 20 since we’re looking for how much we’ll have after 20 years
So 20×12 (round your answer to the nearest penny)
A = 3000(1 + ) = $9930.61
Let us compare the amount of money earned from compounding against the amount you would earn
from simple interest
Simple Interest 6% compounded
Years monthly = 0.5%
($15 per month)
5 $3900 $4046.55
10 $4800 $5458.19
$5700 $7362.28
20 $6600 $9930.61
$7500 $13394.91
$8400 $18067.73
35 $9300 $24370.65
As you can see, over a long period of time, compounding makes a large difference in the account
balance. You may recognize this as the difference between linear growth and exponential growth.
Evaluating exponents on the calculator
When we need to calculate something like 3 it is easy enough to just multiply .
But when we need to calculate something like 240, it would be very tedious to calculate 1.005
this by multiplying 1.005 by itself 240 times! So to make things easier, we can harness the power of
our scientific calculators.
($) 25000
20000
Balance
15000
10000
Account
5000
0
0 5 10 15 20 25 30 35
Years
Most scientific calculators have a button for exponents. It is typically either labeled like:
, x , or [ y ]
