Question 1

Accepted Answer

The graph of a logarithmic function is shown. Select the function which matches the graph.- 
A)    f(x) =log⁡5xf ( x )  = \log _ { 5 } xf(x) =log5​x 
B)    f(x) =log⁡5(x−1) f ( x )  = \log _ { 5 } ( x - 1 ) f(x) =log5​(x−1)  
C)    f(x) =log⁡5x−1f ( x )  = \log _ { 5 } x - 1f(x) =log5​x−1 
D)    f(x) =log⁡5(x+1) f ( x )  = \log _ { 5 } ( x + 1 ) f(x) =log5​(x+1)

Question 2

Solve the problem.
-What principal invested at 8% compounded continuously for 4 years will yield $1190? Round the answer to two decimal places.

Accepted Answer

A)   $1638.78
B)   $1188.62
C)   $864.12
D)   $627.48

Question 3

Solve the problem.
-The logistic growth model  P(t) =4101+40e−0.176tP ( t )  = \frac { 410 } { 1 + 40 e ^ { - 0.176 t } }P(t) =1+40e−0.176t410​  represents the population of a species introduced into a new territory after t years. When will the population be 60?

Accepted Answer

A)   10.94 years
B)   6.34 years
C)   3.69 years
D)   16.76 years

Question 4

Solve the problem.
-The logistic growth functi  f(t) =4401+7.8e−0.17tf ( t )  = \frac { 440 } { 1 + 7.8 e ^ { - 0.17 t } }f(t) =1+7.8e−0.17t440​  describes the population of a species of butterflies t months after they are introduced to a non-threatening habitat. How many butterflies were initially introduced to the
Habitat?

Accepted Answer

A)   2 butterflies
B)   50 butterflies
C)   8 butterflies
D)   440 butterflies

Question 5

Solve the equation.
- 2(7−3x) =142 ^ { ( 7 - 3 x )  } = \frac { 1 } { 4 }2(7−3x) =41​

Accepted Answer

A)    {3}\{ 3 \}{3} 
B)    {−3}\{ - 3 \}{−3} 
C)    {12}\left\{ \frac { 1 } { 2 } \right\}{21​} 
D)    {1}\{ 1 \}{1}

Question 6

Solve the equation.
- log⁡3(3x+7) =log⁡3(3x+2) \log _ { 3 } ( 3 x + 7 )  = \log _ { 3 } ( 3 x + 2 ) log3​(3x+7) =log3​(3x+2)

Accepted Answer

A)    {5}\{ 5 \}{5} 
B)    {0}\{ 0 \}{0} 
C)    ∅\varnothing∅ 
D)    {95}\left\{ \frac { 9 } { 5 } \right\}{59​}

Question 7

Use a graphing calculator to solve the equation. Round your answer to two decimal places.
- log⁡4(x+2) −log⁡5(x−1) =1\log _ { 4 } ( x + 2 )  - \log _ { 5 } ( x - 1 )  = 1log4​(x+2) −log5​(x−1) =1

Accepted Answer

A)   {-0.69}
B)   {2.05}
C)   {1.75}
D)   {1.98}

Question 8

Change the exponential expression to an equivalent expression involving a logarithm.
- 3−2=193 ^ { - 2 } = \frac { 1 } { 9 }3−2=91​

Accepted Answer

A)    log⁡−219=3\log _ { - 2 } \frac { 1 } { 9 } = 3log−2​91​=3 
B)    log⁡1/93=−2\log _ { 1 / 9 } 3 = - 2log1/9​3=−2 
C)    log⁡319=−2\log _ { 3 } \frac { 1 } { 9 } = - 2log3​91​=−2 
D)    log⁡3−2=19\log _ { 3 } - 2 = \frac { 1 } { 9 }log3​−2=91​

Question 9

Accepted Answer

Graph the function.- f(x) =4−e−xf(x) =4-e^{-x}f(x) =4−e−x  
A)  
B)   
C)  
D)

Question 10

Solve the problem.
-How long does it take $1125 to triple if it is invested at 7% interest, compounded quarterly? Round your answer to the nearest tenth.

Accepted Answer

A)   15.8 years
B)   18.1 months
C)   15.8 months
D)   18.1 years

Question 11

Solve the problem.
-The bacteria in a 8-liter container double every 3 minutes. After 57 minutes the container is full. How long did it take to fill a quarter of the container?

Accepted Answer

A)   51 min
B)   42.8 min
C)   28.5 min
D)   14.3 min

Question 12

Use a calculator to find the natural logarithm correct to four decimal places.
- ln⁡(3.64⋅10−8) \ln \left( 3.64 \cdot 10 ^ { - 8 } \right) ln(3.64⋅10−8)

Accepted Answer

A)    −10.3360- 10.3360−10.3360 
B)    −17.1287- 17.1287−17.1287 
C)    1.29201.29201.2920 
D)    3.37143.37143.3714

Question 13

Solve the equation.
-models the average number of free-throws a basketball player can make consecutively during practice as a function of time, where x is the number of consecutive days the basketball
Player has practiced for two hours. After how many days of practice can the basketball player make an average
Of 7 consecutive free throws?

Accepted Answer

A)   149 days
B)   147 days
C)   44 days
D)   42 days

Question 14

Use the horizontal line test to determine whether the function is one-to-one.
-

Accepted Answer

A)   No
B)   Yes

Question 15

Decide whether or not the functions are inverses of each other.
- f(x) =6+xx,g(x) =6x−1f ( x )  = \frac { 6 + x } { x } , g ( x )  = \frac { 6 } { x - 1 }f(x) =x6+x​,g(x) =x−16​

Accepted Answer

A)   Yes
B)   No

Question 16

Use the horizontal line test to determine whether the function is one-to-one.
-

Accepted Answer

A)   Yes
B)   No

Question 17

Solve the equation.
- 8ln⁡3x=408 \ln 3 x = 408ln3x=40

Accepted Answer

A)    {e53}\left\{ \frac { \mathrm { e } ^ { 5 } } { 3 } \right\}{3e5​} 
B)    {e5/3}\left\{ e ^ { 5 / 3 } \right\}{e5/3} 
C)    {5ln⁡3}\left\{ \frac { 5 } { \ln 3 } \right\}{ln35​} 
D)    {e5}\left\{ e ^ { 5 } \right\}{e5}

Question 18

Find the domain of the composite function f  f∘gf ^ { \circ } g f∘g 
- f(x) =x;g(x) =5x+10f ( x )  = \sqrt { x } ; \quad g ( x )  = 5 x + 10f(x) =x​;g(x) =5x+10

Accepted Answer

A)    {x∣x≥0}\{ x \mid x \geq 0 \}{x∣x≥0} 
B)    {x∣x≤−2\{ x \mid x \leq - 2{x∣x≤−2  or  x≥0}x \geq 0 \}x≥0} 
C)    {x∣x≥−2}\{ x \mid x \geq - 2 \}{x∣x≥−2} 
D)    {x∣x\{ x \mid x{x∣x  is any real number  }\}}

Question 19

Solve the problem.
-The functio  A=AOe−0.0099x\mathrm { A } = \mathrm { A } _ { \mathrm { O } } \mathrm { e } ^ { - 0.0099 \mathrm { x } }A=AO​e−0.0099x  models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 500 pounds of the
Material are initially put into the vault, how many pounds will be left after 80 years?

Accepted Answer

A)   286 pounds
B)   273 pounds
C)   226 pounds
D)   219 pounds

Question 20

Change the logarithmic expression to an equivalent expression involving an exponent.
- log⁡1024256=45\log _ { 1024 } 256 = \frac { 4 } { 5 }log1024​256=54​

Accepted Answer

A)    2564/5=1024256 ^ { 4 / 5 } = 10242564/5=1024 
B)    2565/4=1024256 ^ { 5 / 4 } = 10242565/4=1024 
C)    (45) 1024=256\left( \frac { 4 } { 5 } \right)  ^ { 1024 } = 256(54​) 1024=256 
D)    10244/5=2561024 ^ { 4 / 5 } = 25610244/5=256

Exam 4: Exponential and Logarithmic Functions

Solve the problem. -How long does it take $1125 to triple if it is invested at 7% interest, compounded quarterly? Round your answer to the nearest tenth.

Correct Answer
verified

Use a graphing calculator to solve the equation. Round your answer to two decimal places. - $\log _ { 4 } ( x + 2 ) - \log _ { 5 } ( x - 1 ) = 1$

Correct Answer
verified

Correct Answer
verified

Solve the equation. - $2 ^ { ( 7 - 3 x ) } = \frac { 1 } { 4 }$

Correct Answer
verified

Decide whether or not the functions are inverses of each other. - $f ( x ) = \frac { 6 + x } { x } , g ( x ) = \frac { 6 } { x - 1 }$

Correct Answer
verified

Change the exponential expression to an equivalent expression involving a logarithm. - $3 ^ { - 2 } = \frac { 1 } { 9 }$

Correct Answer
verified

Solve the problem. -The logistic growth model $P ( t ) = \frac { 410 } { 1 + 40 e ^ { - 0.176 t } }$ represents the population of a species introduced into a new territory after t years. When will the population be 60?

Correct Answer
verified

Solve the equation. - $8 \ln 3 x = 40$

Correct Answer
verified

Solve the equation. - $\log _ { 3 } ( 3 x + 7 ) = \log _ { 3 } ( 3 x + 2 )$

Correct Answer
verified

Use a calculator to find the natural logarithm correct to four decimal places. - $\ln \left( 3.64 \cdot 10 ^ { - 8 } \right)$

Correct Answer
verified

Use the horizontal line test to determine whether the function is one-to-one. -

Correct Answer
verified

Use the horizontal line test to determine whether the function is one-to-one. -

Correct Answer
verified

Solve the problem. -The bacteria in a 8-liter container double every 3 minutes. After 57 minutes the container is full. How long did it take to fill a quarter of the container?

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Solve the problem. -What principal invested at 8% compounded continuously for 4 years will yield $1190? Round the answer to two decimal places.

Correct Answer
verified

Solve the problem. -The logistic growth functi $f ( t ) = \frac { 440 } { 1 + 7.8 e ^ { - 0.17 t } }$ describes the population of a species of butterflies t months after they are introduced to a non-threatening habitat. How many butterflies were initially introduced to the Habitat?

Correct Answer
verified

Find the domain of the composite function f $f ^ { \circ } g$ - $f ( x ) = \sqrt { x } ; \quad g ( x ) = 5 x + 10$

Correct Answer
verified

Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { 1024 } 256 = \frac { 4 } { 5 }$

Correct Answer
verified

Exam 4: Exponential and Logarithmic Functions

Solve the problem. -How long does it take $1125 to triple if it is invested at 7% interest, compounded quarterly? Round your answer to the nearest tenth.

Correct AnswerverifiedShow Answer

Use a graphing calculator to solve the equation. Round your answer to two decimal places. - log⁡4(x+2) −log⁡5(x−1) =1\log _ { 4 } ( x + 2 ) - \log _ { 5 } ( x - 1 ) = 1log4​(x+2) −log5​(x−1) =1

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Solve the equation. - 2(7−3x) =142 ^ { ( 7 - 3 x ) } = \frac { 1 } { 4 }2(7−3x) =41​

Correct AnswerverifiedShow Answer

Decide whether or not the functions are inverses of each other. - f(x) =6+xx,g(x) =6x−1f ( x ) = \frac { 6 + x } { x } , g ( x ) = \frac { 6 } { x - 1 }f(x) =x6+x​,g(x) =x−16​

Correct AnswerverifiedShow Answer

Change the exponential expression to an equivalent expression involving a logarithm. - 3−2=193 ^ { - 2 } = \frac { 1 } { 9 }3−2=91​

Correct AnswerverifiedShow Answer

Solve the problem. -The logistic growth model P(t) =4101+40e−0.176tP ( t ) = \frac { 410 } { 1 + 40 e ^ { - 0.176 t } }P(t) =1+40e−0.176t410​ represents the population of a species introduced into a new territory after t years. When will the population be 60?

Correct AnswerverifiedShow Answer

Solve the equation. - 8ln⁡3x=408 \ln 3 x = 408ln3x=40

Correct AnswerverifiedShow Answer

Solve the equation. - log⁡3(3x+7) =log⁡3(3x+2) \log _ { 3 } ( 3 x + 7 ) = \log _ { 3 } ( 3 x + 2 ) log3​(3x+7) =log3​(3x+2)

Correct AnswerverifiedShow Answer

Use a calculator to find the natural logarithm correct to four decimal places. - ln⁡(3.64⋅10−8) \ln \left( 3.64 \cdot 10 ^ { - 8 } \right) ln(3.64⋅10−8)

Correct AnswerverifiedShow Answer

Use the horizontal line test to determine whether the function is one-to-one. -

Correct AnswerverifiedShow Answer

Use the horizontal line test to determine whether the function is one-to-one. -

Correct AnswerverifiedShow Answer

Solve the problem. -The bacteria in a 8-liter container double every 3 minutes. After 57 minutes the container is full. How long did it take to fill a quarter of the container?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Solve the problem. -What principal invested at 8% compounded continuously for 4 years will yield $1190? Round the answer to two decimal places.

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Find the domain of the composite function f f∘gf ^ { \circ } g f∘g - f(x) =x;g(x) =5x+10f ( x ) = \sqrt { x } ; \quad g ( x ) = 5 x + 10f(x) =x​;g(x) =5x+10

Correct AnswerverifiedShow Answer

Change the logarithmic expression to an equivalent expression involving an exponent. - log⁡1024256=45\log _ { 1024 } 256 = \frac { 4 } { 5 }log1024​256=54​

Correct AnswerverifiedShow Answer

Correct Answer
verified

Use a graphing calculator to solve the equation. Round your answer to two decimal places. - $\log _ { 4 } ( x + 2 ) - \log _ { 5 } ( x - 1 ) = 1$

Correct Answer
verified

Correct Answer
verified

Solve the equation. - $2 ^ { ( 7 - 3 x ) } = \frac { 1 } { 4 }$

Correct Answer
verified

Decide whether or not the functions are inverses of each other. - $f ( x ) = \frac { 6 + x } { x } , g ( x ) = \frac { 6 } { x - 1 }$

Correct Answer
verified

Change the exponential expression to an equivalent expression involving a logarithm. - $3 ^ { - 2 } = \frac { 1 } { 9 }$

Correct Answer
verified

Solve the problem. -The logistic growth model $P ( t ) = \frac { 410 } { 1 + 40 e ^ { - 0.176 t } }$ represents the population of a species introduced into a new territory after t years. When will the population be 60?

Correct Answer
verified

Solve the equation. - $8 \ln 3 x = 40$

Correct Answer
verified

Solve the equation. - $\log _ { 3 } ( 3 x + 7 ) = \log _ { 3 } ( 3 x + 2 )$

Correct Answer
verified

Use a calculator to find the natural logarithm correct to four decimal places. - $\ln \left( 3.64 \cdot 10 ^ { - 8 } \right)$

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Find the domain of the composite function f $f ^ { \circ } g$ - $f ( x ) = \sqrt { x } ; \quad g ( x ) = 5 x + 10$

Correct Answer
verified

Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { 1024 } 256 = \frac { 4 } { 5 }$

Correct Answer
verified