Question 1

Solve the problem.
-The logistic growth function  f(t) =4401+5.3e−0.24tf ( t )  = \frac { 440 } { 1 + 5.3 e ^ { - 0.24 t } }f(t) =1+5.3e−0.24t440​  describes the population of a species of butterflies t months after they are introduced to a non-threatening habitat. What is the limiting size of the butterfly population that the habitat will sustain?

Accepted Answer

A)   440 butterflies
B)   70 butterflies
C)   5 butterflies
D)   880 butterflies

Question 2

Solve the problem.
-Find out how long it takes a  $2700\$ 2700$2700  investment to earn  $300\$ 300$300  interest if it is invested at  7%7 \%7%  compounded quarterly. Round to the nearest tenth of a year. Use the formula  A=P(1+rn) nt\mathrm { A } = \mathrm { P } \left( 1 + \frac { \mathrm { r } } { \mathrm { n } } \right)  ^ { \mathrm { n } t }A=P(1+nr​) nt .

Accepted Answer

A)    1.51.51.5  years
B)    1.71.71.7  years
C)    1.31.31.3  years
D)    1.91.91.9  years

Question 3

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
- log⁡3(9x−1) \log _ { 3 } \left( \frac { 9 } { \sqrt { x - 1 } } \right) log3​(x−1​9​)

Accepted Answer

A)    2−12log⁡3(x−1) 2 - \frac { 1 } { 2 } \log _ { 3 } ( x - 1 ) 2−21​log3​(x−1)  
B)    2log⁡33−12log⁡3(x−1) 2 \log _ { 3 } 3 - \frac { 1 } { 2 } \log _ { 3 } ( x - 1 ) 2log3​3−21​log3​(x−1)  
C)    log⁡39−log⁡3x−1\log _ { 3 } 9 - \log _ { 3 } \sqrt { x - 1 }log3​9−log3​x−1c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
D)    2−log⁡3x−12 - \log _ { 3 } \sqrt { x - 1 }2−log3​x−1c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​

Question 4

Solve the problem.
-The logistic growth function  f(t) =57,0001+813.3e−1.6t\mathrm { f } ( \mathrm { t } )  = \frac { 57,000 } { 1 + 813.3 \mathrm { e } ^ { - 1.6 \mathrm { t } } }f(t) =1+813.3e−1.6t57,000​  models the number of people who have become ill with a particular infection  ttt  weeks after its initial outbreak in a particular community. How many people became ill with this infection when the epidemic began?

Accepted Answer

A)   70 people
B)   57,000 people
C)   813 people
D)   814 people

Question 5

Write the equation in its equivalent logarithmic form.
- c4=20,736c ^ { 4 } = 20,736c4=20,736

Accepted Answer

A)    log⁡C20,736=4\log _ { \mathrm { C } } 20,736 = 4logC​20,736=4 
B)    log⁡20,736c=4\log _ { 20,736 } \mathrm { c } = 4log20,736​c=4 
C)    log⁡420,736=c\log _ { 4 } 20,736 = clog4​20,736=c 
D)    log⁡C4=20,736\log _ { \mathrm { C } } 4 = 20,736logC​4=20,736

Question 6

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
- log⁡7(m5n6k2) \log _ { 7 } \left( \frac { \sqrt [ 5 ] { m } \sqrt [ 6 ] { n } } { k ^ { 2 } } \right) log7​(k25m​6n​​)

Accepted Answer

A)    15log⁡7 m+16log⁡7n−2log⁡7k\frac { 1 } { 5 } \log _ { 7 } \mathrm {~m} + \frac { 1 } { 6 } \log _ { 7 } \mathrm { n } - 2 \log _ { 7 } \mathrm { k }51​log7​ m+61​log7​n−2log7​k 
B)    15log⁡7 m⋅16log⁡7n÷2log⁡7k\frac { 1 } { 5 } \log _ { 7 } \mathrm {~m} \cdot \frac { 1 } { 6 } \log _ { 7 } \mathrm { n } \div 2 \log _ { 7 } \mathrm { k }51​log7​ m⋅61​log7​n÷2log7​k 
C)    57log⁡7 m+67log⁡7n−27log⁡7k\frac { 5 } { 7 } \log _ { 7 } \mathrm {~m} + \frac { 6 } { 7 } \log _ { 7 } \mathrm { n } - \frac { 2 } { 7 } \log _ { 7 } \mathrm { k }75​log7​ m+76​log7​n−72​log7​k 
D)    5log⁡7 m+6log⁡7n−2log⁡7k5 \log _ { 7 } \mathrm {~m} + 6 \log _ { 7 } \mathrm { n } - 2 \log _ { 7 } \mathrm { k }5log7​ m+6log7​n−2log7​k

Question 7

Solve the problem.
-Use the formula  R=log⁡(aT) +B\mathrm { R } = \log \left( \frac { \mathrm { a } } { \mathrm { T } } \right)  + \mathrm { B }R=log(Ta​) +B  to find the intensity  R\mathrm { R }R  on the Richter scale, given that amplitude a is 207 micrometers, time  T\mathrm { T }T  between waves is  3.53.53.5  seconds, and  B\mathrm { B }B  is 2.7. Round answer to one decimal place.

Accepted Answer

A)    4.54.54.5 
B)    6.86.86.8 
C)    1.81.81.8 
D)   7

Question 8

Use Natural Logarithms
Evaluate or simplify the expression without using a calculator.
- eln⁡112\mathrm { e } ^ { \ln 112 }eln112

Accepted Answer

A)   112
B)    −112- 112−112 
C)    e112\mathrm { e } ^ { 112 }e112 
D)    ln⁡112\ln 112ln112

Question 9

Use the Definition of a Logarithm to Solve Logarithmic Equations
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic
expressions. Give the exact answer.
- log⁡2(x+1) −log⁡2(x−3) =4\log _ { 2 } ( x + 1 )  - \log _ { 2 } ( x - 3 )  = 4log2​(x+1) −log2​(x−3) =4

Accepted Answer

A)    {4915}\left\{ \frac { 49 } { 15 } \right\}{1549​} 
B)    {415}\left\{ \frac { 4 } { 15 } \right\}{154​} 
C)    {−4915}\left\{ - \frac { 49 } { 15 } \right\}{−1549​} 
D)    ∅\varnothing∅  )

Question 10

Graph the function.
-Use the graph of  f(x) =3xf ( x )  = 3 ^ { x }f(x) =3x  to obtain the graph of  g(x) =3−xg ( x )  = 3 ^ { - x }g(x) =3−x .

Accepted Answer

A)  
B)  
C)  
D)

Question 11

Graph the function.
-Use the graph of  f(x) =2xf ( x )  = 2 ^ { x }f(x) =2x  to obtain the graph of  g(x) =2⋅2xg ( x )  = 2 \cdot 2 ^ { x }g(x) =2⋅2x .

Accepted Answer

A)  
B)  
C)  
D)

Question 12

Graph the function.
-Use the graph of  f(x) =exf ( x )  = e ^ { x }f(x) =ex  to obtain the graph of  g(x) =2exg ( x )  = 2 e ^ { x }g(x) =2ex .

Accepted Answer

A)  
B)  
C)  
D)

Question 13

Evaluate or simplify the expression without using a calculator.
- 10log⁡x410 \log \sqrt [ 4 ] { x }10log4x​

Accepted Answer

A)    x1/4x ^ { 1 / 4 }x1/4 
B)    x4x ^ { 4 }x4 
C)   4
D)    x−1/4x ^ { - 1 / 4 }x−1/4

Question 14

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm
whose coefficient is 1. Where possible, evaluate logarithmic expressions.
- log⁡x+log⁡(x2−4) −log⁡3−log⁡(x−2) \log x + \log \left( x ^ { 2 } - 4 \right)  - \log 3 - \log ( x - 2 ) logx+log(x2−4) −log3−log(x−2)

Accepted Answer

A)    log⁡x(x+2) 3\log \frac { x ( x + 2 )  } { 3 }log3x(x+2) ​ 
B)    log⁡x(x−4) 3(x−2) \log \frac { x ( x - 4 )  } { 3 ( x - 2 )  }log3(x−2) x(x−4) ​ 
C)    log⁡x(x−4) (x−2) 3\log \frac { x ( x - 4 )  ( x - 2 )  } { 3 }log3x(x−4) (x−2) ​ 
D)    log⁡2x+2) 5−x\log \frac { 2 x + 2 )  } { 5 - x }log5−x2x+2) ​

Question 15

Use the One-to-One Property of Logarithms to Solve Logarithmic Equations
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic
expressions. Give the exact answer.
- log⁡3x=log⁡4+log⁡(x−3) \log 3 x = \log 4 + \log ( x - 3 ) log3x=log4+log(x−3)

Accepted Answer

A)    {12}\{ 12 \}{12} 
B)    {12}\left\{ \frac { 1 } { 2 } \right\}{21​} 
C)    {−12}\{ - 12 \}{−12} 
D)    {−127}\left\{ - \frac { 12 } { 7 } \right\}{−712​}

Question 16

Find the domain of the logarithmic function.
- f(x) =log⁡9(x+8) f ( x )  = \log _ { 9 } ( x + 8 ) f(x) =log9​(x+8)

Accepted Answer

A)    (−8,∞) ( - 8 , \infty ) (−8,∞)  
B)    (9,∞) ( 9 , \infty ) (9,∞)  
C)    (8,∞) ( 8 , \infty ) (8,∞)  
D)    (−∞,0) ( - \infty , 0 ) (−∞,0)   or  (0,∞) ( 0 , \infty ) (0,∞)

Question 17

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
- log⁡3(7⋅1113) \log _ { 3 } \left( \frac { 7 \cdot 11 } { 13 } \right) log3​(137⋅11​)

Accepted Answer

A)    log⁡37+log⁡311−log⁡313\log _ { 3 } 7 + \log _ { 3 } 11 - \log _ { 3 } 13log3​7+log3​11−log3​13 
B)    log⁡3(7713) \log _ { 3 } \left( \frac { 77 } { 13 } \right) log3​(1377​)  
C)    log⁡377−log⁡313\log _ { 3 } 77 - \log _ { 3 } 13log3​77−log3​13 
D)    log⁡35\log _ { 3 } 5log3​5

Question 18

Use Compound Interest Formulas
Use the compound interest formulas A  A=P(1+rn)  and A=Pert to solve A = P \left( 1 + \frac { r } { n } ight)  	ext { and } A = P e ^ { r t } 	ext { to solve }A=P(1+nr​)  and A=Pert to solve  
-Find the accumulated value of an investment of $1230 at 6% compounded annually for 5 years.

Accepted Answer

A)  $1646.02
B)  $1552.85
C)  $1525.20
D)  $1599.00

Question 19

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places,
for the solution.
- e2x+ex−6=0e ^ { 2 x } + e ^ { x } - 6 = 0e2x+ex−6=0

Accepted Answer

A)    0.690.690.69 
B)    0.69,1.100.69,1.100.69,1.10 
C)    1.10,0.141.10,0.141.10,0.14 
D)    0.140.140.14

Question 20

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places,
for the solution.
- 25x=3.72 ^ { 5 x } = 3.725x=3.7

Accepted Answer

A)    0.380.380.38 
B)    0.410.410.41 
C)    9.449.449.44 
D)    8.598.598.59

Exam 4: Exponential and Logarithmic Functions

Correct Answer
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Write the equation in its equivalent logarithmic form. - $c ^ { 4 } = 20,736$

Correct Answer
verified

Use the One-to-One Property of Logarithms to Solve Logarithmic Equations Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - $\log 3 x = \log 4 + \log ( x - 3 )$

Correct Answer
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Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $e ^ { 2 x } + e ^ { x } - 6 = 0$

Correct Answer
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Find the domain of the logarithmic function. - $f ( x ) = \log _ { 9 } ( x + 8 )$

Correct Answer
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Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $\log x + \log \left( x ^ { 2 } - 4 \right) - \log 3 - \log ( x - 2 )$

Correct Answer
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Correct Answer
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Graph the function. -Use the graph of $f ( x ) = e ^ { x }$ to obtain the graph of $g ( x ) = 2 e ^ { x }$ . $Graph the function. -Use the graph of f ( x ) = e ^ { x } to obtain the graph of g ( x ) = 2 e ^ { x } . A) B) C) D)$

Correct Answer
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Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 3 } \left( \frac { 7 \cdot 11 } { 13 } \right)$

Correct Answer
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Correct Answer
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Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $2 ^ { 5 x } = 3.7$

Correct Answer
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Evaluate or simplify the expression without using a calculator. - $10 \log \sqrt [ 4 ] { x }$

Correct Answer
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Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 7 } \left( \frac { \sqrt [ 5 ] { m } \sqrt [ 6 ] { n } } { k ^ { 2 } } \right)$

Correct Answer
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Use Natural Logarithms Evaluate or simplify the expression without using a calculator. - $\mathrm { e } ^ { \ln 112 }$

Correct Answer
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Graph the function. -Use the graph of $f ( x ) = 2 ^ { x }$ to obtain the graph of $g ( x ) = 2 \cdot 2 ^ { x }$ . $Graph the function. -Use the graph of f ( x ) = 2 ^ { x } to obtain the graph of g ( x ) = 2 \cdot 2 ^ { x } . A) B) C) D)$

Correct Answer
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Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 3 } \left( \frac { 9 } { \sqrt { x - 1 } } \right)$

Correct Answer
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Correct Answer
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Graph the function. -Use the graph of $f ( x ) = 3 ^ { x }$ to obtain the graph of $g ( x ) = 3 ^ { - x }$ . $Graph the function. -Use the graph of f ( x ) = 3 ^ { x } to obtain the graph of g ( x ) = 3 ^ { - x } . A) B) C) D)$

Correct Answer
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Use the Definition of a Logarithm to Solve Logarithmic Equations Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - $\log _ { 2 } ( x + 1 ) - \log _ { 2 } ( x - 3 ) = 4$

Correct Answer
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Use Compound Interest Formulas Use the compound interest formulas A $A = P \left( 1 + \frac { r } { n } \right) \text { and } A = P e ^ { r t } \text { to solve }$ -Find the accumulated value of an investment of $1230 at 6% compounded annually for 5 years.

Correct Answer
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Exam 4: Exponential and Logarithmic Functions

Correct AnswerverifiedShow Answer

Write the equation in its equivalent logarithmic form. - c4=20,736c ^ { 4 } = 20,736c4=20,736

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - e2x+ex−6=0e ^ { 2 x } + e ^ { x } - 6 = 0e2x+ex−6=0

Correct AnswerverifiedShow Answer

Find the domain of the logarithmic function. - f(x) =log⁡9(x+8) f ( x ) = \log _ { 9 } ( x + 8 ) f(x) =log9​(x+8)

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Graph the function. -Use the graph of f(x) =exf ( x ) = e ^ { x }f(x) =ex to obtain the graph of g(x) =2exg ( x ) = 2 e ^ { x }g(x) =2ex .

Correct AnswerverifiedShow Answer

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡3(7⋅1113) \log _ { 3 } \left( \frac { 7 \cdot 11 } { 13 } \right) log3​(137⋅11​)

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - 25x=3.72 ^ { 5 x } = 3.725x=3.7

Correct AnswerverifiedShow Answer

Evaluate or simplify the expression without using a calculator. - 10log⁡x410 \log \sqrt [ 4 ] { x }10log4x​

Correct AnswerverifiedShow Answer

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡7(m5n6k2) \log _ { 7 } \left( \frac { \sqrt [ 5 ] { m } \sqrt [ 6 ] { n } } { k ^ { 2 } } \right) log7​(k25m​6n​​)

Correct AnswerverifiedShow Answer

Use Natural Logarithms Evaluate or simplify the expression without using a calculator. - eln⁡112\mathrm { e } ^ { \ln 112 }eln112

Correct AnswerverifiedShow Answer

Graph the function. -Use the graph of f(x) =2xf ( x ) = 2 ^ { x }f(x) =2x to obtain the graph of g(x) =2⋅2xg ( x ) = 2 \cdot 2 ^ { x }g(x) =2⋅2x .

Correct AnswerverifiedShow Answer

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡3(9x−1) \log _ { 3 } \left( \frac { 9 } { \sqrt { x - 1 } } \right) log3​(x−1​9​)

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Graph the function. -Use the graph of f(x) =3xf ( x ) = 3 ^ { x }f(x) =3x to obtain the graph of g(x) =3−xg ( x ) = 3 ^ { - x }g(x) =3−x .

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct Answer
verified

Write the equation in its equivalent logarithmic form. - $c ^ { 4 } = 20,736$

Correct Answer
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Correct Answer
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Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $e ^ { 2 x } + e ^ { x } - 6 = 0$

Correct Answer
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Find the domain of the logarithmic function. - $f ( x ) = \log _ { 9 } ( x + 8 )$

Correct Answer
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Correct Answer
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Correct Answer
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Graph the function. -Use the graph of $f ( x ) = e ^ { x }$ to obtain the graph of $g ( x ) = 2 e ^ { x }$ . $Graph the function. -Use the graph of f ( x ) = e ^ { x } to obtain the graph of g ( x ) = 2 e ^ { x } . A) B) C) D)$

Correct Answer
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Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 3 } \left( \frac { 7 \cdot 11 } { 13 } \right)$

Correct Answer
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Correct Answer
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Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $2 ^ { 5 x } = 3.7$

Correct Answer
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Evaluate or simplify the expression without using a calculator. - $10 \log \sqrt [ 4 ] { x }$

Correct Answer
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Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 7 } \left( \frac { \sqrt [ 5 ] { m } \sqrt [ 6 ] { n } } { k ^ { 2 } } \right)$

Correct Answer
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Use Natural Logarithms Evaluate or simplify the expression without using a calculator. - $\mathrm { e } ^ { \ln 112 }$

Correct Answer
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Graph the function. -Use the graph of $f ( x ) = 2 ^ { x }$ to obtain the graph of $g ( x ) = 2 \cdot 2 ^ { x }$ . $Graph the function. -Use the graph of f ( x ) = 2 ^ { x } to obtain the graph of g ( x ) = 2 \cdot 2 ^ { x } . A) B) C) D)$

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Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 3 } \left( \frac { 9 } { \sqrt { x - 1 } } \right)$

Correct Answer
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Correct Answer
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Graph the function. -Use the graph of $f ( x ) = 3 ^ { x }$ to obtain the graph of $g ( x ) = 3 ^ { - x }$ . $Graph the function. -Use the graph of f ( x ) = 3 ^ { x } to obtain the graph of g ( x ) = 3 ^ { - x } . A) B) C) D)$

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Correct Answer
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Correct Answer
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