Question 1

Solve the problem.
-The Feldmans bought their first house for $14,000. Over the years they moved three times into bigger and bigger houses. Now, 41 years later, they are ready to retire and want a smaller house like the first one they
Bought. If inflation in property values has averaged 3.6% per year during that time, how much will such a
House cost them now? (Round your answer to the nearest dollar.)

Accepted Answer

A)   $3,284
B)   $3,200
C)   $61,256
D)   $59,687E) None of the above
F) A) and B)

Question 2

Accepted Answer

The graph of an exponential function is given. Match the graph to one of the following functions.- 
A)    y=0.65xy = 0.65 ^ { x }y=0.65x 
B)    y=0.32xy = 0.32 ^ { x }y=0.32x 
C)    y=2.4xy = 2.4 ^ { x }y=2.4x 
D)    y=3.5xy = 3.5 ^ { x }y=3.5xE) All of the above
F) C) and D)

Question 3

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator.
- log⁡440−log⁡410\log _ { 4 } 40 - \log _ { 4 } 10log4​40−log4​10

Accepted Answer

A)   4
B)   10
C)   40
D)   1 E) A) and B)
F) C) and D)

Question 4

Accepted Answer

The graph of a logarithmic function is shown. Select the function which matches the graph.- 
A)    y=3−log⁡(x) y = 3 - \log ( x ) y=3−log(x)  
B)    y=log⁡(x−3) y = \log ( x - 3 ) y=log(x−3)  
C)    y=log⁡(x) −3y = \log ( x )  - 3y=log(x) −3 
D)    y=log⁡(3−x) y = \log ( 3 - x ) y=log(3−x) E) B) and C)
F) C) and D)

Question 5

Express as a single logarithm.
-  0">ln⁡x2+4x−32x−3−ln⁡x2+5x−24x+3+ln⁡(x2−8x+16) ,x>0\ln \frac { x ^ { 2 } + 4 x - 32 } { x - 3 } - \ln \frac { x ^ { 2 } + 5 x - 24 } { x + 3 } + \ln \left( x ^ { 2 } - 8 x + 16 \right)  , \quad x > 0lnx−3x2+4x−32​−lnx+3x2+5x−24​+ln(x2−8x+16) ,x>0

Accepted Answer

A)    ln⁡3(x−4) 2(x−3) (x+3) \ln \frac { 3 ( x - 4 )  } { 2 ( x - 3 )  ( x + 3 )  }ln2(x−3) (x+3) 3(x−4) ​ 
B)    ln⁡(x−4) 3(x−3) 2(x+3) \ln \frac { ( x - 4 )  ^ { 3 } } { ( x - 3 )  ^ { 2 } ( x + 3 )  }ln(x−3) 2(x+3) (x−4) 3​ 
C)    ln⁡(x−4) 3(x+3) (x−3) 2\ln \frac { ( x - 4 )  ^ { 3 } ( x + 3 )  } { ( x - 3 )  ^ { 2 } }ln(x−3) 2(x−4) 3(x+3) ​ 
D)    ln⁡3(x−4) (x+3) 2(x−3) \ln \frac { 3 ( x - 4 )  ( x + 3 )  } { 2 ( x - 3 )  }ln2(x−3) 3(x−4) (x+3) ​E) C) and D)
F) A) and B)

Question 6

Find the domain of the function.
- f(x) =log⁡1/2(x+4) f ( x )  = \log _ { 1 / 2 } ( x + 4 ) f(x) =log1/2​(x+4)

Accepted Answer

A)    (−∞,−4) ( - \infty , - 4 ) (−∞,−4)  
B)    (−4,∞) ( - 4 , \infty ) (−4,∞)  
C)    (4,∞) ( 4 , \infty ) (4,∞)  
D)    (−∞,4) ( - \infty , 4 ) (−∞,4) E) A) and D)
F) B) and C)

Question 7

Solve the equation.
- 2x2−3=642 ^ { x ^ { 2 } - 3 } = 642x2−3=64

Accepted Answer

A)    {3}\{ 3 \}{3} 
B)    {35,−35}\{ \sqrt { 35 } , - \sqrt { 35 } \}{35c-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'/>​,−35c-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'/>​} 
C)    {6}\{ 6 \}{6} 
D)    {3,−3}\{ 3 , - 3 \}{3,−3}E) B) and D)
F) C) and D)

Question 8

Solve the problem.
-The logistic growth functi  f(t) =12,0001+199e−1.7tf ( t )  = \frac { 12,000 } { 1 + 199 e ^ { - 1.7 t } }f(t) =1+199e−1.7t12,000​  models the number of people who have become ill with a particular infection t weeks after its initial outbreak in a particular community. How many people were ill after
9 weeks?

Accepted Answer

A)   12,000 people
B)   11,999 people
C)   12,200 people
D)   540 people E) A) and D)
F) B) and C)

Question 9

Accepted Answer

Graph the function.- f(x) =ex+5f ( x )  = e ^ { x + 5 }f(x) =ex+5  
A)  
B)   
C)  
D)   E) B) and D)
F) undefined

Question 10

Express as a single logarithm.
- 28log⁡7x7+log⁡7(28x6) −log⁡72828 \log _ { 7 } \sqrt [ 7 ] { x } + \log _ { 7 } \left( 28 x ^ { 6 } \right)  - \log _ { 7 } 2828log7​7x​+log7​(28x6) −log7​28

Accepted Answer

A)    log⁡7x10/7\log _ { 7 } x ^ { 10 / 7 }log7​x10/7 
B)    log⁡7x13/4\log _ { 7 } x ^ {13 / 4}log7​x13/4 
C)    log⁡7x10\log _ { 7 }x ^ {10}log7​x10 
D)    log⁡7x11/6\log _ { 7 } \mathrm { x } ^ { 11 / 6 }log7​x11/6E) A) and D)
F) A) and B)

Question 11

Choose the one alternative that best completes the statement or answers the question.
Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the
solution.
- (12) x=15\left( \frac { 1 } { 2 } \right)  ^ { x } = 15(21​) x=15

Accepted Answer

A)   {-0.26}
B)   {-7.50}
C)   {3.91}
D)   {-3.91} E) A) and D)
F) All of the above

Question 12

The function f is one-to-one. Find its inverse.
- f(x) =5x+43f ( x )  = \frac { 5 x + 4 } { 3 }f(x) =35x+4​

Accepted Answer

A)    f−1(x) =35x+4f ^ { - 1 } ( x )  = \frac { 3 } { 5 x + 4 }f−1(x) =5x+43​ 
B)    f−1(x) =35x−4f ^ { - 1 } ( x )  = \frac { 3 } { 5 x - 4 }f−1(x) =5x−43​ 
C)    f−1(x) =3x−45f ^ { - 1 } ( x )  = \frac { 3 x - 4 } { 5 }f−1(x) =53x−4​ 
D)    f−1(x) =3x+45\mathrm { f } ^ { - 1 } ( \mathrm { x } )  = \frac { 3 \mathrm { x } + 4 } { 5 }f−1(x) =53x+4​E) None of the above
F) A) and B)

Question 13

Accepted Answer

Graph the function using a graphing utility and the Change-of-Base Formula.- y=log⁡3(x−2) y = \log _ { 3 } ( x - 2 ) y=log3​(x−2)   
A)  
B)   
C)  
D)   E) B) and D)
F) undefined

Question 14

Write as the sum and/or difference of logarithms. Express powers as factors.
- log⁡(1−1x3) \log \left( 1 - \frac { 1 } { x ^ { 3 } } \right) log(1−x31​)

Accepted Answer

A)    log⁡(x−1) +log⁡(x2+1) −3log⁡x\log ( x - 1 )  + \log \left( x ^ { 2 } + 1 \right)  - 3 \log xlog(x−1) +log(x2+1) −3logx 
B)    log⁡1−3log⁡1−3log⁡x\log 1 - 3 \log 1 - 3 \log xlog1−3log1−3logx 
C)    log⁡(x−1) +log⁡(x2+x+1) −3log⁡x\log ( x - 1 )  + \log \left( x ^ { 2 } + x + 1 \right)  - 3 \log xlog(x−1) +log(x2+x+1) −3logx 
D)    log⁡x3−log⁡1−3log⁡x\log x ^ { 3 } - \log 1 - 3 \log xlogx3−log1−3logxE) None of the above
F) All of the above

Question 15

Decide whether or not the functions are inverses of each other.
- f(x) =8x−9,g(x) =x+89f ( x )  = 8 x - 9 , g ( x )  = \frac { x + 8 } { 9 }f(x) =8x−9,g(x) =9x+8​

Accepted Answer

A)   No
B)   Yes C) A) and B)
D) undefined

Question 16

Solve the equation.
- log⁡(3x) =log⁡5+log⁡(x−4) \log ( 3 x )  = \log 5 + \log ( x - 4 ) log(3x) =log5+log(x−4)

Accepted Answer

A)    {−52}\left\{ - \frac { 5 } { 2 } \right\}{−25​} 
B)    {12}\left\{ \frac { 1 } { 2 } \right\}{21​} 
C)    {−10}\{ - 10 \}{−10} 
D)    {10}\{ 10 \}{10}E) All of the above
F) B) and C)

Question 17

Solve the problem.
-The logistic growth model  P(t) =1,4501+28e−0.313tP ( t )  = \frac { 1,450 } { 1 + 28 e ^ { - 0.313 t } }P(t) =1+28e−0.313t1,450​  represents the population of a bacterium in a culture tube after t hours. What was the initial amount of bacteria in the population?

Accepted Answer

A)   55
B)   50
C)   49
D)   51 E) A) and D)
F) A) and C)

Question 18

Find the domain of the composite function f  f∘gf ^ { \circ } g f∘g 
- f(x) =2−x;g(x) =∣2x−1∣f ( x )  = \sqrt { 2 - x } ; \quad g ( x )  = | 2 x - 1 |f(x) =2−x​;g(x) =∣2x−1∣

Accepted Answer

A)    {x∣x≤2}\{ x \mid x \leq 2 \}{x∣x≤2} 
B)    {x∣x≥2}\{ x \mid x \geq 2 \}{x∣x≥2} 
C)    {x∣−12≤x≤32}\left\{ x \mid - \frac { 1 } { 2 } \leq x \leq \frac { 3 } { 2 } \right\}{x∣−21​≤x≤23​} 
D)   all real numbers E) C) and D)
F) A) and B)

Question 19

Express as a single logarithm.
- 8log⁡b8+9log⁡b38 \log _ { b } 8 + 9 \log _ { b } 38logb​8+9logb​3

Accepted Answer

A)    log⁡b88⋅log⁡b39\log _ { \mathrm { b } } 88 \cdot \log _ { \mathrm { b } } 3 ^ { 9 }logb​88⋅logb​39 
B)    log⁡b8839\log _ { b } 883 ^ { 9 }logb​8839 
C)    log⁡b(64+27) \log _ { b } ( 64 + 27 ) logb​(64+27)  
D)    log⁡b8839\log _ { b } \frac { 88 } { 3 ^ { 9 } }logb​3988​E) All of the above
F) A) and B)

Question 20

The function f is one-to-one. Find its inverse.
- f(x) =x+53f ( x )  = \sqrt [ 3 ] { x + 5 }f(x) =3x+5​

Accepted Answer

A)    f−1(x) =x3−5f ^ { - 1 } ( x )  = x ^ { 3 } - 5f−1(x) =x3−5 
B)    f−1(x) =1x3−5f ^ { - 1 } ( x )  = \frac { 1 } { x ^ { 3 } - 5 }f−1(x) =x3−51​ 
C)    f−1(x) =x3+25f ^ { - 1 } ( x )  = x ^ { 3 } + 25f−1(x) =x3+25 
D)    f−1(x) =x−5f ^ { - 1 } ( x )  = x - 5f−1(x) =x−5E) A) and B)
F) C) and D)

Exam 4: Exponential and Logarithmic Functions

Correct Answer
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Correct Answer
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The function f is one-to-one. Find its inverse. - $f ( x ) = \frac { 5 x + 4 } { 3 }$

Correct Answer
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Decide whether or not the functions are inverses of each other. - $f ( x ) = 8 x - 9 , g ( x ) = \frac { x + 8 } { 9 }$

Correct Answer
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Solve the problem. -The logistic growth functi $f ( t ) = \frac { 12,000 } { 1 + 199 e ^ { - 1.7 t } }$ models the number of people who have become ill with a particular infection t weeks after its initial outbreak in a particular community. How many people were ill after 9 weeks?

Correct Answer
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Correct Answer
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Find the domain of the composite function f $f ^ { \circ } g$ - $f ( x ) = \sqrt { 2 - x } ; \quad g ( x ) = | 2 x - 1 |$

Correct Answer
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Find the domain of the function. - $f ( x ) = \log _ { 1 / 2 } ( x + 4 )$

Correct Answer
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Solve the equation. - $2 ^ { x ^ { 2 } - 3 } = 64$

Correct Answer
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Correct Answer
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Write as the sum and/or difference of logarithms. Express powers as factors. - $\log \left( 1 - \frac { 1 } { x ^ { 3 } } \right)$

Correct Answer
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Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - $\log _ { 4 } 40 - \log _ { 4 } 10$

Correct Answer
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Express as a single logarithm. - $28 \log _ { 7 } \sqrt [ 7 ] { x } + \log _ { 7 } \left( 28 x ^ { 6 } \right) - \log _ { 7 } 28$

Correct Answer
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The function f is one-to-one. Find its inverse. - $f ( x ) = \sqrt [ 3 ] { x + 5 }$

Correct Answer
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Solve the equation. - $\log ( 3 x ) = \log 5 + \log ( x - 4 )$

Correct Answer
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Correct Answer
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Express as a single logarithm. - $8 \log _ { b } 8 + 9 \log _ { b } 3$

Correct Answer
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Solve the problem. -The logistic growth model $P ( t ) = \frac { 1,450 } { 1 + 28 e ^ { - 0.313 t } }$ represents the population of a bacterium in a culture tube after t hours. What was the initial amount of bacteria in the population?

Correct Answer
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Choose the one alternative that best completes the statement or answers the question. Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $\left( \frac { 1 } { 2 } \right) ^ { x } = 15$

Correct Answer
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Express as a single logarithm. - $\ln \frac { x ^ { 2 } + 4 x - 32 } { x - 3 } - \ln \frac { x ^ { 2 } + 5 x - 24 } { x + 3 } + \ln \left( x ^ { 2 } - 8 x + 16 \right) , \quad x > 0$

Correct Answer
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Exam 4: Exponential and Logarithmic Functions

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

The function f is one-to-one. Find its inverse. - f(x) =5x+43f ( x ) = \frac { 5 x + 4 } { 3 }f(x) =35x+4​

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Decide whether or not the functions are inverses of each other. - f(x) =8x−9,g(x) =x+89f ( x ) = 8 x - 9 , g ( x ) = \frac { x + 8 } { 9 }f(x) =8x−9,g(x) =9x+8​

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Find the domain of the composite function f f∘gf ^ { \circ } g f∘g - f(x) =2−x;g(x) =∣2x−1∣f ( x ) = \sqrt { 2 - x } ; \quad g ( x ) = | 2 x - 1 |f(x) =2−x​;g(x) =∣2x−1∣

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Find the domain of the function. - f(x) =log⁡1/2(x+4) f ( x ) = \log _ { 1 / 2 } ( x + 4 ) f(x) =log1/2​(x+4)

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Solve the equation. - 2x2−3=642 ^ { x ^ { 2 } - 3 } = 642x2−3=64

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Correct AnswerverifiedShow Answer

Write as the sum and/or difference of logarithms. Express powers as factors. - log⁡(1−1x3) \log \left( 1 - \frac { 1 } { x ^ { 3 } } \right) log(1−x31​)

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Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - log⁡440−log⁡410\log _ { 4 } 40 - \log _ { 4 } 10log4​40−log4​10

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Express as a single logarithm. - 28log⁡7x7+log⁡7(28x6) −log⁡72828 \log _ { 7 } \sqrt [ 7 ] { x } + \log _ { 7 } \left( 28 x ^ { 6 } \right) - \log _ { 7 } 2828log7​7x​+log7​(28x6) −log7​28

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The function f is one-to-one. Find its inverse. - f(x) =x+53f ( x ) = \sqrt [ 3 ] { x + 5 }f(x) =3x+5​

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Solve the equation. - log⁡(3x) =log⁡5+log⁡(x−4) \log ( 3 x ) = \log 5 + \log ( x - 4 ) log(3x) =log5+log(x−4)

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Correct AnswerverifiedShow Answer

Express as a single logarithm. - 8log⁡b8+9log⁡b38 \log _ { b } 8 + 9 \log _ { b } 38logb​8+9logb​3

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Solve the problem. -The logistic growth model P(t) =1,4501+28e−0.313tP ( t ) = \frac { 1,450 } { 1 + 28 e ^ { - 0.313 t } }P(t) =1+28e−0.313t1,450​ represents the population of a bacterium in a culture tube after t hours. What was the initial amount of bacteria in the population?

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Choose the one alternative that best completes the statement or answers the question. Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - (12) x=15\left( \frac { 1 } { 2 } \right) ^ { x } = 15(21​) x=15

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Correct AnswerverifiedShow Answer

Correct Answer
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Correct Answer
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The function f is one-to-one. Find its inverse. - $f ( x ) = \frac { 5 x + 4 } { 3 }$

Correct Answer
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Decide whether or not the functions are inverses of each other. - $f ( x ) = 8 x - 9 , g ( x ) = \frac { x + 8 } { 9 }$

Correct Answer
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Correct Answer
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Correct Answer
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Find the domain of the composite function f $f ^ { \circ } g$ - $f ( x ) = \sqrt { 2 - x } ; \quad g ( x ) = | 2 x - 1 |$

Correct Answer
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Find the domain of the function. - $f ( x ) = \log _ { 1 / 2 } ( x + 4 )$

Correct Answer
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Solve the equation. - $2 ^ { x ^ { 2 } - 3 } = 64$

Correct Answer
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Correct Answer
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Write as the sum and/or difference of logarithms. Express powers as factors. - $\log \left( 1 - \frac { 1 } { x ^ { 3 } } \right)$

Correct Answer
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Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - $\log _ { 4 } 40 - \log _ { 4 } 10$

Correct Answer
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Express as a single logarithm. - $28 \log _ { 7 } \sqrt [ 7 ] { x } + \log _ { 7 } \left( 28 x ^ { 6 } \right) - \log _ { 7 } 28$

Correct Answer
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The function f is one-to-one. Find its inverse. - $f ( x ) = \sqrt [ 3 ] { x + 5 }$

Correct Answer
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Solve the equation. - $\log ( 3 x ) = \log 5 + \log ( x - 4 )$

Correct Answer
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Correct Answer
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Express as a single logarithm. - $8 \log _ { b } 8 + 9 \log _ { b } 3$

Correct Answer
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Solve the problem. -The logistic growth model $P ( t ) = \frac { 1,450 } { 1 + 28 e ^ { - 0.313 t } }$ represents the population of a bacterium in a culture tube after t hours. What was the initial amount of bacteria in the population?

Correct Answer
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Choose the one alternative that best completes the statement or answers the question. Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $\left( \frac { 1 } { 2 } \right) ^ { x } = 15$

Correct Answer
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Correct Answer
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