Question 1

Solve the equation.
-$3 \cdot 5 ^ { 2 t - 1 } = 75$

Accepted Answer

A)  $\{ 3 \}$ 
B)  $\left\{ \frac { 1 } { 2 } \right\}$ 
C)  $\left\{ \frac { 13 } { 10 } \right\}$ 
D)  $\left\{ \frac { 3 } { 2 } \right\}$ 
A)  $\{ 3 \}$ 
B)  $\left\{ \frac { 1 } { 2 } \right\}$ 
C)  $\left\{ \frac { 13 } { 10 } \right\}$ 
D)  $\left\{ \frac { 3 } { 2 } \right\}$

Question 2

For the given functions f and g, find the requested composite function value.
-$f ( x ) = 4 x + 6 , \quad g ( x ) = 4 x ^ { 2 } + 3 ; \quad$ Find $( g \circ f ) ( 3 )$

Accepted Answer

A)  6,087 
B)  78 
C)  162 
D)  1,299 
A)  6,087 
B)  78 
C)  162 
D)  1,299

Question 3

Use a calculator to find the natural logarithm correct to four decimal places.
-In $0.983$

Accepted Answer

A)  $0.0171$ 
B)  $- 0.0171$ 
C)  $- 0.0074$ 
D)  $0.0074$ 
A)  $0.0171$ 
B)  $- 0.0171$ 
C)  $- 0.0074$ 
D)  $0.0074$

Question 4

Choose the one alternative that best completes the statement or answers the question.
-Cindy will require $12,000 in 5 years to return to college to get an MBA degree. How much money should she ask her parents for now so that, if she invests it at 11% compounded continuously, she will have enough for
School? (Round your answer to the nearest dollar.)

Accepted Answer

A)  $3,994 
B)  $7,121 
C)  $6,923 
D)  $20,799 
A)  $3,994 
B)  $7,121 
C)  $6,923 
D)  $20,799

Question 5

Change the exponential expression to an equivalent expression involving a logarithm.
-$$7 ^ { 3 } = x$$

Accepted Answer

A)  $\log _ { 3 } x = 7$ 
B)  $\log _ { x } 7 = 3$ 
C)  $\log _ { 7 } x = 3$ 
D)  $\log _ { 7 } 3 = x$ 
A)  $\log _ { 3 } x = 7$ 
B)  $\log _ { x } 7 = 3$ 
C)  $\log _ { 7 } x = 3$ 
D)  $\log _ { 7 } 3 = x$

Question 6

Decide whether the composite functions, f ° g and g ° f, are equal to x.
-$$f ( x ) = \frac { x - 6 } { 4 } , \quad g ( x ) = 4 x + 6$$

Accepted Answer

A)  Yes, yes 
B)  No, yes 
C)  No, no 
D)  Yes, no 
A)  Yes, yes 
B)  No, yes 
C)  No, no 
D)  Yes, no

Question 7

Write the word or phrase that best completes each statement or answers the question.
-$$3 ^ { 2 x } + 3 ^ { x } - 6 = 0$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 8

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

Accepted Answer

A)  $\left\{ - \frac { 5 } { 2 } \right\}$ 
B)  $\left\{ \frac { 1 } { 2 } \right\}$ 
C)  $\{ - 10 \}$ 
D)  $\{ 10 \}$ 
A)  $\left\{ - \frac { 5 } { 2 } \right\}$ 
B)  $\left\{ \frac { 1 } { 2 } \right\}$ 
C)  $\{ - 10 \}$ 
D)  $\{ 10 \}$

Question 9

Solve the equation.
-$$\log _ { 6 } ( x + 3 ) = 3$$

Accepted Answer

A)  $\{ 732 \}$ 
B)  $\{ 726 \}$ 
C)  $\{ 219 \}$ 
D)  $\{ 213 \}$ 
A)  $\{ 732 \}$ 
B)  $\{ 726 \}$ 
C)  $\{ 219 \}$ 
D)  $\{ 213 \}$

Question 10

Use transformations to graph the function.
-$$\text { Use the graph of } \log _ { 4 } x \text { to obtain the graph of } f ( x ) = - 1 + \log _ { 4 } x \text {. }$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 11

Solve the problem.
-Find the amount owed at the end of 8 years if $\$ 5000$ is loaned at a rate of $5 \%$ compounded monthly.

Accepted Answer

A)  $\$ 8060.16$ 
B)  $\$ 12,911.25$ 
C)  $\$ 7452.93$ 
D)  $\$ 9093.60$ 
A)  $\$ 8060.16$ 
B)  $\$ 12,911.25$ 
C)  $\$ 7452.93$ 
D)  $\$ 9093.60$

Question 12

Solve the given exponential equation. Round answer to three decimal places.
-$$5 ^ { 2 x } + 5 ( x + 1 ) - 24 = 0$$

Accepted Answer

A)  $\{ 0.683 \}$ 
B)  $\{ 1.147 \}$ 
C)  $\{ 1.099 \}$ 
D)  $\{ 1.292 \}$ 
A)  $\{ 0.683 \}$ 
B)  $\{ 1.147 \}$ 
C)  $\{ 1.099 \}$ 
D)  $\{ 1.292 \}$

Question 13

Write the word or phrase that best completes each statement or answers the question.
-$$y = \log _ { 61 } x$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 14

Write the word or phrase that best completes each statement or answers the question.
-Meike earned $1565 in tips while working a summer job at a coffee shop. She wants to use this money to take a
trip to Europe next summer. If she places the money in an account which pays 6.5% compounded continuously,
how much money will she have in nine months?

Accepted Answer

The answer of Write the word or phrase that best...

Question 15

Express y as a function of x. The constant C is a positive number.
-$\ln y = \ln 4 x + \ln C$

Accepted Answer

A)  $y = x + 4 C$ 
B)  $y = ( 4 x ) ^ { C }$ 
C)  $y = 4 x + C$ 
D)  $y = 4 C x$ 
A)  $y = x + 4 C$ 
B)  $y = ( 4 x ) ^ { C }$ 
C)  $y = 4 x + C$ 
D)  $y = 4 C x$

Question 16

Solve the problem.
-The formula $\mathrm { P } = 14.7 \mathrm { e } ^ { - 0.21 \mathrm { x } }$ gives the average atmospheric pressure, $\mathrm { P }$, in pounds per square inch, at an altitude $x$, in miles above sea level. Find the average atmospheric pressure for an altitude of $2.3$ miles. Round your answer to the nearest tenth.

Accepted Answer

A)  $7.8 \mathrm { lb } / \mathrm { in } ^ { 2 }$ 
B)  $9.1 \mathrm { lb } / \mathrm { in } ^ { 2 }$ 
C)  $8.4 \mathrm { lb } /$ in. $^ { 2 }$ 
D)  $11.0 \mathrm { lb } /$ in. $^ { 2 }$ 
A)  $7.8 \mathrm { lb } / \mathrm { in } ^ { 2 }$ 
B)  $9.1 \mathrm { lb } / \mathrm { in } ^ { 2 }$ 
C)  $8.4 \mathrm { lb } /$ in. $^ { 2 }$ 
D)  $11.0 \mathrm { lb } /$ in. $^ { 2 }$

Question 17

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places.
-$\log _ { 3.2 } 57$

Accepted Answer

A)  $3.476$ 
B)  $1.756$ 
C)  $17.813$ 
D)  $0.288$ 
A)  $3.476$ 
B)  $1.756$ 
C)  $17.813$ 
D)  $0.288$

Question 18

Find the inverse of the function and state its domain and range .
-$$\{ ( 9 , - 8 ) , ( 7 , - 7 ) , ( 5 , - 6 ) , ( 3 , - 5 ) \}$$

Accepted Answer

A)  $\{ ( - 7 , - 8 ) , ( - 8,5 ) , ( 9,7 ) , ( - 7 , - 6 ) \} ; \mathrm { D } = \{ ( - 7 , - 8,9 \} ; \mathrm { R } = \{ ( - 8,57 , - 6 \}$ 
B)  $\{ ( - 8,9 ) , ( - 7,7 ) , ( - 6,5 ) , ( - 5,3 ) \} ; \mathrm { D } = \{ - 8 , - 7 , - 6 , - 5 \} ; \mathrm { R } = \{ 9,7,5,3 \}$ 
C)  $\{ ( - 7 , - 8 ) , ( - 5,5 ) , ( 9,5 ) , ( - 7 , - 6 ) \} ; \mathrm { D } = \{ - 7 , - 5,9 \} ; \mathrm { R } = \{ - 8,5 , - 6 \}$ 
D)  $\left\{ \left( 9 , - \frac { 1 } { 8 } \right) , \left( 7 , - \frac { 1 } { 7 } \right\} , \left( 5 , - \frac { 1 } { 6 } \right) , \left( 3 , - \frac { 1 } { 5 } \right) \right\} ; \mathrm { D } = \{ 9,7,5,3 \} , \mathrm { R } = \left\{ - \frac { 1 } { 8 } , - \frac { 1 } { 7 } , - \frac { 1 } { 6 } , - \frac { 1 } { 5 } \right\}$ 
A)  $\{ ( - 7 , - 8 ) , ( - 8,5 ) , ( 9,7 ) , ( - 7 , - 6 ) \} ; \mathrm { D } = \{ ( - 7 , - 8,9 \} ; \mathrm { R } = \{ ( - 8,57 , - 6 \}$ 
B)  $\{ ( - 8,9 ) , ( - 7,7 ) , ( - 6,5 ) , ( - 5,3 ) \} ; \mathrm { D } = \{ - 8 , - 7 , - 6 , - 5 \} ; \mathrm { R } = \{ 9,7,5,3 \}$ 
C)  $\{ ( - 7 , - 8 ) , ( - 5,5 ) , ( 9,5 ) , ( - 7 , - 6 ) \} ; \mathrm { D } = \{ - 7 , - 5,9 \} ; \mathrm { R } = \{ - 8,5 , - 6 \}$ 
D)  $\left\{ \left( 9 , - \frac { 1 } { 8 } \right) , \left( 7 , - \frac { 1 } { 7 } \right\} , \left( 5 , - \frac { 1 } { 6 } \right) , \left( 3 , - \frac { 1 } { 5 } \right) \right\} ; \mathrm { D } = \{ 9,7,5,3 \} , \mathrm { R } = \left\{ - \frac { 1 } { 8 } , - \frac { 1 } { 7 } , - \frac { 1 } { 6 } , - \frac { 1 } { 5 } \right\}$

Question 19

Choose the one alternative that best completes the statement or answers the question.
-A life insurance company uses the following rate table for annual premiums for women for term life insurance. Use a graphing utility to fit an exponential function to the data. Predict the annual premium for a woman aged 70 years.
$\begin{array}{l|lllllll}
\text { Age } & 35 & 40 & 45 & 50 & 55 & 60 & 65 \
\hline \text { Premium } & \$ 103 & \$ 133 & \$ 190 & \$ 255 & \$ 360 & \$ 503 & \$ 818
\end{array}$

Accepted Answer

A)  $y = 0.0000398 x ^ { 4.06 } , \$ 1233$ 
B)  $y = 8.94 \mathrm { e } ^ { 0.068 x , } \$ 1044$ 
C)  $y = 6.367 \mathrm { e } ^ { 0.068 \mathrm { x } } , \$ 743$ 
D)  $y = - 9306.4 + 2516.3 \ln ( x ) , \$ 1723$ 
A)  $y = 0.0000398 x ^ { 4.06 } , \$ 1233$ 
B)  $y = 8.94 \mathrm { e } ^ { 0.068 x , } \$ 1044$ 
C)  $y = 6.367 \mathrm { e } ^ { 0.068 \mathrm { x } } , \$ 743$ 
D)  $y = - 9306.4 + 2516.3 \ln ( x ) , \$ 1723$

Question 20

Solve the equation.
-$$125 ^ { x } = 625$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 3 } \right\}$ 
B)  $\left\{ \frac { 4 } { 3 } \right\}$ 
C)  $\left\{ \frac { 3 } { 4 } \right\}$ 
D)  $\left\{ \frac { 1 } { 4 } \right\}$ 
A)  $\left\{ \frac { 1 } { 3 } \right\}$ 
B)  $\left\{ \frac { 4 } { 3 } \right\}$ 
C)  $\left\{ \frac { 3 } { 4 } \right\}$ 
D)  $\left\{ \frac { 1 } { 4 } \right\}$

Solve the equation. - $3 \cdot 5 ^ { 2 t - 1 } = 75$

For the given functions f and g, find the requested composite function value. - $f ( x ) = 4 x + 6 , \quad g ( x ) = 4 x ^ { 2 } + 3 ; \quad$ Find $( g \circ f ) ( 3 )$

Use a calculator to find the natural logarithm correct to four decimal places. -In $0.983$

Change the exponential expression to an equivalent expression involving a logarithm. - $7 ^ { 3 } = x$

Decide whether the composite functions, f ° g and g ° f, are equal to x. - $f ( x ) = \frac { x - 6 } { 4 } , \quad g ( x ) = 4 x + 6$

Write the word or phrase that best completes each statement or answers the question. - $3 ^ { 2 x } + 3 ^ { x } - 6 = 0$

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

Solve the equation. - $\log _ { 6 } ( x + 3 ) = 3$

Solve the problem. -Find the amount owed at the end of 8 years if $\$ 5000$ is loaned at a rate of $5 \%$ compounded monthly.

Solve the given exponential equation. Round answer to three decimal places. - $5 ^ { 2 x } + 5 ( x + 1 ) - 24 = 0$

Write the word or phrase that best completes each statement or answers the question. - $y = \log _ { 61 } x$

Express y as a function of x. The constant C is a positive number. - $\ln y = \ln 4 x + \ln C$

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places. - $\log _ { 3.2 } 57$

Find the inverse of the function and state its domain and range . - $\{ ( 9 , - 8 ) , ( 7 , - 7 ) , ( 5 , - 6 ) , ( 3 , - 5 ) \}$

Solve the equation. - $125 ^ { x } = 625$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 4: Exponential and Logarithmic Functions

Solve the equation. - 3⋅52t−1=753 \cdot 5 ^ { 2 t - 1 } = 753⋅52t−1=75

For the given functions f and g, find the requested composite function value. - f(x)=4x+6,g(x)=4x2+3;f ( x ) = 4 x + 6 , \quad g ( x ) = 4 x ^ { 2 } + 3 ; \quadf(x)=4x+6,g(x)=4x2+3; Find (g∘f)(3)( g \circ f ) ( 3 )(g∘f)(3)

Use a calculator to find the natural logarithm correct to four decimal places. -In 0.9830.9830.983

Change the exponential expression to an equivalent expression involving a logarithm. - 73=x7 ^ { 3 } = x73=x

Decide whether the composite functions, f ° g and g ° f, are equal to x. - f(x)=x−64,g(x)=4x+6f ( x ) = \frac { x - 6 } { 4 } , \quad g ( x ) = 4 x + 6f(x)=4x−6​,g(x)=4x+6

Write the word or phrase that best completes each statement or answers the question. - 32x+3x−6=03 ^ { 2 x } + 3 ^ { x } - 6 = 032x+3x−6=0

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

Solve the equation. - log⁡6(x+3)=3\log _ { 6 } ( x + 3 ) = 3log6​(x+3)=3

Use transformations to graph the function. - Use the graph of log⁡4x to obtain the graph of f(x)=−1+log⁡4x. \text { Use the graph of } \log _ { 4 } x \text { to obtain the graph of } f ( x ) = - 1 + \log _ { 4 } x \text {. } Use the graph of log4​x to obtain the graph of f(x)=−1+log4​x.

Solve the problem. -Find the amount owed at the end of 8 years if $5000\$ 5000$5000 is loaned at a rate of 5%5 \%5% compounded monthly.

Solve the given exponential equation. Round answer to three decimal places. - 52x+5(x+1)−24=05 ^ { 2 x } + 5 ( x + 1 ) - 24 = 052x+5(x+1)−24=0

Write the word or phrase that best completes each statement or answers the question. - y=log⁡61xy = \log _ { 61 } xy=log61​x

Express y as a function of x. The constant C is a positive number. - ln⁡y=ln⁡4x+ln⁡C\ln y = \ln 4 x + \ln Clny=ln4x+lnC

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places. - log⁡3.257\log _ { 3.2 } 57log3.2​57

Find the inverse of the function and state its domain and range . - {(9,−8),(7,−7),(5,−6),(3,−5)}\{ ( 9 , - 8 ) , ( 7 , - 7 ) , ( 5 , - 6 ) , ( 3 , - 5 ) \}{(9,−8),(7,−7),(5,−6),(3,−5)}

Solve the equation. - 125x=625125 ^ { x } = 625125x=625

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Solve the equation. - $3 \cdot 5 ^ { 2 t - 1 } = 75$

For the given functions f and g, find the requested composite function value. - $f ( x ) = 4 x + 6 , \quad g ( x ) = 4 x ^ { 2 } + 3 ; \quad$ Find $( g \circ f ) ( 3 )$

Use a calculator to find the natural logarithm correct to four decimal places. -In $0.983$

Change the exponential expression to an equivalent expression involving a logarithm. - $7 ^ { 3 } = x$

Decide whether the composite functions, f ° g and g ° f, are equal to x. - $f ( x ) = \frac { x - 6 } { 4 } , \quad g ( x ) = 4 x + 6$

Write the word or phrase that best completes each statement or answers the question. - $3 ^ { 2 x } + 3 ^ { x } - 6 = 0$

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

Solve the equation. - $\log _ { 6 } ( x + 3 ) = 3$

Solve the problem. -Find the amount owed at the end of 8 years if $\$ 5000$ is loaned at a rate of $5 \%$ compounded monthly.

Solve the given exponential equation. Round answer to three decimal places. - $5 ^ { 2 x } + 5 ( x + 1 ) - 24 = 0$

Write the word or phrase that best completes each statement or answers the question. - $y = \log _ { 61 } x$

Express y as a function of x. The constant C is a positive number. - $\ln y = \ln 4 x + \ln C$

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places. - $\log _ { 3.2 } 57$

Find the inverse of the function and state its domain and range . - $\{ ( 9 , - 8 ) , ( 7 , - 7 ) , ( 5 , - 6 ) , ( 3 , - 5 ) \}$

Solve the equation. - $125 ^ { x } = 625$