Lee, Amanda
5.2: Practicing Percent Change and Modeling Exponential Growth (Lesson)
Started: November 13, 2019, 9:42 pm
Last change: November 13, 2019, 10:07 pm
Time spent: 25 minutes
Total time questions were on-screen: 24.8 minutes.
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Grade Book Detail
A company’s premium house paint used to cost $35 per gallon. After a recent price increase,
their premium house paint now costs $50.75 per gallon. See the following diagram.
Complete the following statements.
a. The new price is how many times as large as the old price?
$
1.45
b. What is the change in the price per gallon from the original price to the new price (in
dollars)?
$
15.75
c. What is the percent change in the price per gallon? (That is, the change amount from part
(b) is what percent of the original price?)
45
%
Question 1: 3 out of 3 in 2 attempt(s)
a. Andrea's annual salary was $46,200, but she was recently given a raise. Her new annual
salary is $50,358. Complete the following statements.
i. Andrea's new annual salary is
1.09
times as large as her
previous annual salary.
ii. Andrea's new annual salary is
109
% of her previous annual
salary.
iii. Andrea's new annual salary changed by
9
% of her previous
annual salary. Hint
b. Kevin's annual salary is $54,500 and Maggie's annual salary is $68,670. Which of the
following are true statements? Select all that apply.
Maggie's salary is 1.26 times as large as Kevin's salary.
Maggie's salary is 126% of Kevin's salary.
Maggie's salary is $14,170 more than Kevin's salary.
Maggie's salary is 79% of Kevin's salary.
Maggie's salary is 0.79 times as large as Kevin's salary.
Question 2: 3 out of 3 in 1 attempt(s)
The following table represents values for an exponential function f where y=f x .
x y =f x
−1 100
0 120
1 144
2 172.8
3 207.36
4.5 227.15
5.5 272.58
Use the table to complete the following.
a. The value of the ratio is
1.2
.
b. The value of the ratio is
1.2
.
c. The value of the ratio is
1.2
.
d. The 1-unit growth factor for this exponential function is
1.2
.
e. The 1-unit percent change for this exponential function is
20
%.
Question 3: 3 out of 3 in 1 attempt(s)
( )
( )
f0( )
f1( )
f2( )
f3( )
f4.5( )
f5.5( )
From 2010-2020 the median home value in the city of Fort William grew exponentially. The
median home value during this time period changed by 12% per year.
a. If the 1-year percent change is 12%, what is the 1-year growth factor?
1.12
b. Use your answer to part (a) to complete the following table of values showing the median
home value in Fort William at various times.
years since the beginning of 2010,
t
median home value in Fort William (in
dollars)
0 182,400
1 204,288
2
228803
3.25 263,623
4.25
295258
5.25
330689
c. Define a function f that models the median home value in Fort William t years since the
beginning of 2010 (assuming 0 ≤ t≤ 10). Be sure to use function notation.
f(t)=182400(1.12)^t
Question 4: 3 out of 3 in 1 attempt(s)
A city's population grows exponentially by 5% per year.
a. What is the 1-year growth factor for the population?
1.05
b. Fill in the missing information in the table below.
years since the beginning of 2015, nthe city's population, p=g n
0 160,000
1 168,000
2
176400
4.25 196,800
5.25
206700
c. Define a function g to model the city's population n years since the beginning of 2015.
g(n)=160000(1.05)^n
Question 5: 3 out of 3 in 1 attempt(s)
( )
The given table of values represents an exponential function (that is, a relationship where the
growth factor is constant for the same size changes in x).
x y =f x
-1 384
0 576
1 864
2 1,296
a. Use the entries in the table to determine the 1-unit growth factor for y in this relationship.
The 1-unit growth factor is
1.5
.
b. The 1-unit percent change for values of y is
50
%
c. Define a formula for function f. Be sure to use function notation.
f(x)=576(1.5)^x
d. Fill in the missing entries in the table. Note: Pay close attention to how the values of x
change. Not all changes are 1 unit. You can also use the formula you defined.
x y =f x
-1 384
0 576
1 864
2 1,296
3
1944
5
4374
8
14,762.25
Question 6: 3 out of 3 in 1 attempt(s)
( )
( )
The graph of an exponential relationship is shown in the following applet. It represents the mass
of bacteria (in micrograms) in an experiment based on the number of hours since noon today.
Drag the purple X on the horizontal axis to vary the
initial number of hours since noon.
a. Vary the value of t by sliding the purple "X" on the horizontal axis. As you do, think about
what the lengths of the blue segments represent and pay attention to the values of the
ordered pairs in the top right corner.
b. What is the 1-hour growth factor in the bacteria mass? (Round your answer to two decimal
places to account for rounding errors in the applet.)
The 1-hour growth factor is
1.26
.
c. What is the 1-hour percent change based on your answer in part (a)?
26
%
d. Define a function h to model the bacteria mass (in micrograms) t hours since noon. Be
sure to use function notation. You will need to use the applet to determine the initial
bacteria mass.
h(t)=10(1.26)^t
Question 7: 3 out of 3 in 1 attempt(s)
12345
25
20
15
10
5
mass of bacteria
hours since noon
1
Pi
Pf
Pi = (0.00, 10.00)
Pf = (1.00, 12.60)
The following graph shows a relationship where y varies exponentially with respect to x.
Drag the purple X on the x-axis to vary the value of
x. The coordinates of the two points are shown at the
top of the applet.
a. Vary the value of x by sliding the purple "X" on the horizontal axis. As you do, think
about what the lengths of the blue segments represent and pay attention to the values of
the ordered pairs displayed at the top.
b. What is the 1-unit growth factor for y? (Round your answer to two decimal places to
account for rounding errors in the applet.)
The 1-unit growth factor is
1.35
.
c. What is the 1-unit percent change based on your answer in part (a)?
35
%
d. Define a function f to model this relationship where y=f x . Be sure to use function
notation. You will need to use the applet to determine the initial bacteria mass.
f(x)=1.25(1.35)^x
Question 8: 3 out of 3 in 1 attempt(s)
( )
x
-1 54321
y
5
4
3
2
1
1
Pi
Pf
Pi = (1.00, 1.69)
Pf = (2.00, 2.28)
The applet below shows four different graphs of exponential functions. Use the slider at the top-
right of the applet to change which graph is shown.
Use the slider at the top-right of the applet to change which
function graph is shown.
Which of the graphs shows an exponential function with a 1-unit percent change of 80%? Select
all that apply (there may be more than one).
Graph A
Graph B
Graph C
Graph D
Question 9: 2 out of 2 in 1 attempt(s)
x
-2 -1 654321
y
-5
35
30
25
20
15
10
5
Graph A
(2, 5)
(3, 9)
(4, 16.2)
(5, 29.16)
Each of the following graphs show a different relationship between x and y. Explore each
relationship and determine the following.
• Is this relationship exponential?
• If the relationship is exponential, is the 1-unit growth factor 1.5?
Make sure to explore each relationship by varying x and observing the relationship
modeled.
a. Is the following an exponential relationship with a 1-unit growth factor of 1.5?
exponential, 1-unit g.f. is NOT 1.5
Drag the purple X on the x-axis to vary the value
of x.
b. Is the following an exponential relationship with a 1-unit growth factor of 1.5?
exponential, 1-unit g.f. is 1.5
x
642
y
12
8
4
(1.00, 3.00)
(2.00, 9.00)
1
Drag the purple X on the x-axis to vary the value
of x.
c. Is the following an exponential relationship with a 1-unit growth factor of 1.5?
not an exponential relationship
Drag the purple X on the x-axis to vary the value
of x.
Question 10: 3 out of 3 in 1 attempt(s)
x
642
y
12
8
4
(1.00, 3.00)
(2.00, 4.50)
1
x
642
y
12
8
4
(1.00, 6.00)
(2.00, 9.00)
1
Total: 29/29
