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5/2/22, 4:16 PM
Quiz: MQ Exponential & Logarithmic Functions - MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=28982970#question3260651_50
2/14
Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions the
population follows a
logistic growth model
:
where
c
,
d
, and
k
are positive constants. For a certain sh population in a small pond
d
= 1400,
k
= 13,
c
= 0.2, and
t
is measured in years. The
sh were introduced into the pond at time
t
= 0.
(a) How many sh were originally put in the pond?
sh
(b) Find the population after 10, 20, and 30 years. (Round your answers to the nearest whole number.)
10 years sh
20 years sh
30 years sh
(c) Evaluate
P
(
t
) for large values of
t
. What value does the population approach as
t
→
∞
?
P
(
t
) =
Does the graph shown conrm your calculations?
Yes
No
Your best entire assignment submission is
used for your score.
P
(
t
) =
d
1 +
ke
−
ct
1.
[–/2 Points] SCOLALG7 4.2.027.MI.
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5/2/22, 4:16 PM
Quiz: MQ Exponential & Logarithmic Functions - MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=28982970#question3260651_50
3/14
Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals.
=
=
=
=
Vilfredo Pareto (1848-1923) observed that most of the wealth of a country is owned by a few members of the population.
Pareto's Principle
is
log(
P
) = log(
c
) −
k
log(
W
)
where
W
is the wealth level (how much money a person has) and
P
is the number of people in the population having that much money.
(a) Solve the equation for
P
.
P
=
(b) Assume
k
= 2.2,
c
= 9000, and
W
is measured in millions of dollars. Use part (a) to nd the number of people who have $2 million
or more. (Round your answer to the nearest whole number.)
people
How many people have $10 million or more? (Round your answer to the nearest whole number.)
people
Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals.
=
=
=
=
f
(
x
) = 7
x
− 1
f
1
2
f
(2.5)
f
(−1)
f
1
4
g
(
x
) = 1
5
x
+ 1
g
1
2
g
( )
6
g
(−2.5)
g
(−1.5)
2.
[–/2 Points] SCOLALG7 4.1.008.
DETAILS
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3.
[–/2 Points] SCOLALG7 4.4.073.MI.
DETAILS
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4.
[–/2 Points] SCOLALG7 4.1.009.
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5/2/22, 4:16 PM
Quiz: MQ Exponential & Logarithmic Functions - MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=28982970#question3260651_50
4/14
Find the solution of the exponential equation, as in Example 1. (Enter your answers as a comma-separated list.)
Express the equation in exponential form.
(a)
(b)
In the formula for continuously compound interest, the letters
P
,
r
, and
t
stand for
---Select---
,
, and
---Select---
, respectively, and
A
(
t
) stands for
---Select---
. So if $300 is invested at an interest rate of 5% compounded continuously, then the amount
after 5 years is $ . (Round your answer to the nearest cent.)
6
x
2
−9
= 6
9−
x
2
x
=
ln(3) = 2
y
ln(
t
+ 2) = −1
A
(
t
) =
Pert
5.
[–/2 Points] SCOLALG7 4.5.009.
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6.
[–/2 Points] SCOLALG7 4.3.015.
DETAILS
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7.
[–/2 Points] SCOLALG7 4.2.002.
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5/2/22, 4:16 PM
Quiz: MQ Exponential & Logarithmic Functions - MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=28982970#question3260651_50
5/14
True or False?
(a) is the same as
True
False
(b) is the same as
True
False
Express the equation in exponential form.
(a)
(b)
log(
x
) is the exponent to which the base 10 must be raised to get
---Select---
. So we can complete the following table for log(
x
).
x
10
3
10
2
10
1
10
0
10
−1
10
−2
10
−3
10
1/2
log(
x
)
The function is called the
---Select---
exponential function. The number
e
is approximately
equal to . (Round your answer to ve decimal places.)
log(
B
+
E
) log(
B
) + log(
E
).
log(
BE
) log(
B
) + log(
E
).
log
3
(7) =
x
log
7
(2
y
) = 5
f
(
x
) =
ex
8.
[–/2 Points] SCOLALG7 4.4.007.
DETAILS
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9.
[–/2 Points] SCOLALG7 4.3.013.
DETAILS
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10.
[–/2 Points] SCOLALG7 4.3.001.
DETAILS
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11.
[–/2 Points] SCOLALG7 4.2.001.
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5/2/22, 4:16 PM
Quiz: MQ Exponential & Logarithmic Functions - MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=28982970#question3260651_50
6/14
A certain breed of mouse was introduced onto a small island with an initial population of 350 mice, and scientists estimate that the mouse
population is doubling every year.
(a) Find a function
N
that models the number of mice after
t
years.
(b) Estimate the mouse population after 7 years.
mice
N
(
t
) =
12.
[–/2 Points] SCOLALG7 4.1.054.
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5/2/22, 4:16 PM
Quiz: MQ Exponential & Logarithmic Functions - MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=28982970#question3260651_50
7/14
Complete the table by nding the appropriate logarithmic or exponential form of the equation, as in Example 1.
Logarithmic
form
Exponential
form
The logarithm of a quotient of two numbers is the same as the
---Select---
of the logarithms of these numbers.
log
8
(8) = 1
log
8
(512) = 3
8
2/3
= 4
8
2
= 64
log
8
= −1
1
8
8
−2
= 1
64
So log
2
= log
2
(4) − .
4
8
13.
[–/2 Points] SCOLALG7 4.3.007.
DETAILS
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14.
[–/2 Points] SCOLALG7 4.4.002.
DETAILS
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5/2/22, 4:16 PM
Quiz: MQ Exponential & Logarithmic Functions - MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=28982970#question3260651_50
8/14
Consider the following.
(a) Find the exact solution of the exponential equation in terms of logarithms.
(b) Use a calculator to nd an approximation to the solution rounded to six decimal places.
Use the Laws of Logarithms to expand the expression.
Use the Laws of Logarithms to combine the expression.
ln(
a
+
b
) + ln(
a
−
b
) − 2 ln(
c
)
The logarithm of a product of two numbers is the same as the
---Select---
of the logarithms of these numbers.
10
x
= 121
x
=
x
=
log
8
(
x
)
y
So log
4
(16
·
64) = log
4
(16) + .
15.
[–/2 Points] SCOLALG7 4.5.011.
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16.
[–/2 Points] SCOLALG7 4.4.032.MI.
DETAILS
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17.
[–/2 Points] SCOLALG7 4.4.055.MI.
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18.
[–/2 Points] SCOLALG7 4.4.001.
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5/2/22, 4:16 PM
Quiz: MQ Exponential & Logarithmic Functions - MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=28982970#question3260651_50
9/14
(a) Convert the following to logarithmic form.
7
4
= 2401
(b) Convert the following to exponential form.
log
7
(49) = 2
This exercise uses the radioactive decay model.
The half-life of strontium-90 is 28 years. How long will it take a 30-mg sample to decay to a mass of 22.8 mg? (Round your answer to the
nearest whole number.)
yr
19.
[–/2 Points] SCOLALG7 4.3.003.
DETAILS
MY NOTES
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20.
[–/2 Points] SCOLALG7 4.6.019.
DETAILS
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5/2/22, 4:16 PM
Quiz: MQ Exponential & Logarithmic Functions - MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=28982970#question3260651_50
10/14
Graph both functions on one set of axes.
f
(
x
) = 3
x
and
g
(
x
) = 8
x
21.
[–/2 Points] SCOLALG7 4.1.019.
DETAILS
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5/2/22, 4:16 PM
Quiz: MQ Exponential & Logarithmic Functions - MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=28982970#question3260651_50
11/14
Graph the function, not by plotting points, but by starting from the graph of in the gure below.
y
=
ex
y
=
e
−
x
−1
22.
[–/2 Points] SCOLALG7 4.2.011.
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5/2/22, 4:16 PM
Quiz: MQ Exponential & Logarithmic Functions - MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=28982970#question3260651_50
12/14
State the domain and range. (Enter your answers using interval notation.)
domain
range
State the asymptote.
5/2/22, 4:16 PM
Quiz: MQ Exponential & Logarithmic Functions - MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=28982970#question3260651_50
13/14
In this exercise we compare the graphs of two exponential functions.
Sketch the graphs of
f
(
x
) = 2
x
and
g
(
x
) = 3(2
x
).
23.
[–/2 Points] SCOLALG7 4.1.041.
DETAILS
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5/2/22, 4:16 PM
Quiz: MQ Exponential & Logarithmic Functions - MATH 121, section D03 (SMITH), Spring 2022 | WebAssign
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=28982970#question3260651_50
14/14
Solve the equation. (Round your answers to four decimal places.)
x
= (smaller value)
x
= (larger value)
This exercise uses the radioactive decay model.
A wooden artifact from an ancient tomb contains 55% of the carbon-14 that is present in living trees. How long ago was the artifact made?
(The half-life of carbon-14 is 5730 years. Round your answer to the nearest whole number.)
yr
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e
2
x
−7
ex
+ 6 = 0
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24.
[–/2 Points] SCOLALG7 4.5.039.MI.
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25.
[–/2 Points] SCOLALG7 4.6.023.
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