Question 1

Solve the equation.
-$$8 ^ { x - 3 } = 64 ^ { 4 x }$$

Accepted Answer

A)  $\left\{ - \frac { 3 } { 7 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 7 } \right\}$ 
C)  $\{ - 1 \}$ 
D)  $\left\{ - \frac { 9 } { 7 } \right\}$ 
A)  $\left\{ - \frac { 3 } { 7 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 7 } \right\}$ 
C)  $\{ - 1 \}$ 
D)  $\left\{ - \frac { 9 } { 7 } \right\}$

Question 2

For the given functions f and g, find the requested composite function value.
-$f ( x ) = \left| 20 x ^ { 2 } - 4 x \right| , \quad g ( x ) = 12 x - 4 ; \quad$ Find $( f \circ g ) ( 4 )$.

Accepted Answer

A)  34,900 
B)  38,544 
C)  3,644 
D)  13,376 
A)  34,900 
B)  38,544 
C)  3,644 
D)  13,376

Question 3

Find the domain of the function.
-$$f ( x ) = \ln ( - 4 - x )$$

Accepted Answer

A)  $x  4$ 
C)  $x  - 4$ 
A)  $x  4$ 
C)  $x  - 4$

Question 4

Solve the problem.
-An airline charter service charges a fare per person of $350 plus $20 for each unsold seat. The airplane holds 125 passengers. Let x represent the number of unsold seats and write an expression for the total revenue R for a
Charter flight.

Accepted Answer

A)  R(x) = (125 - x)(350 + 20x) or 43,750 + 2,150x - 20x2 
B)  R(x) = 125(350 + 20x) or 43,750 + 2,500x 
C)  R(x) = x(350 + 20x) or 350x + 20x2 
D)  R(x) = (125 - x)(350 + 20x) or 43,750 + 2,500x - 20x2 
A)  R(x) = (125 - x)(350 + 20x) or 43,750 + 2,150x - 20x2 
B)  R(x) = 125(350 + 20x) or 43,750 + 2,500x 
C)  R(x) = x(350 + 20x) or 350x + 20x2 
D)  R(x) = (125 - x)(350 + 20x) or 43,750 + 2,500x - 20x2

Question 5

Find the inverse of the function and state its domain and range .
-$$\{ ( - 5 , - 3 ) , ( 3,5 ) , ( 1,1 ) , ( - 1 , - 1 ) \}$$

Accepted Answer

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

Question 6

Approximate the value using a calculator. Express answer rounded to three decimal places.
-$3 ^ { 3.3 }$

Accepted Answer

A)  $27.000$ 
B)  $37.541$ 
C)  $35.937$ 
D)  $9.900$ 
A)  $27.000$ 
B)  $37.541$ 
C)  $35.937$ 
D)  $9.900$

Question 7

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$\log _ { 20 } \left( x ^ { 2 } - x \right) = 1$

Accepted Answer

A)  $\{ - 4,5 \}$ 
B)  $\{ 4,5 \}$ 
C)  $\{ - 4 , - 5 \}$ 
D)  $\{ 1,20 \}$ 
A)  $\{ - 4,5 \}$ 
B)  $\{ 4,5 \}$ 
C)  $\{ - 4 , - 5 \}$ 
D)  $\{ 1,20 \}$

Question 8

Choose the one alternative that best completes the statement or answers the question.
Graph the function using a graphing utility and the Change-of-Base Formula.
-$\log _{x}-5(x+5)$

Accepted Answer

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

Question 9

The graph of an exponential function is given. Match the graph to one of the following functions.
-

Accepted Answer

A)  $f ( x ) = - 4 ^ { x }$ 
B)  $f ( x ) = 4 ^ { - x }$ 
C)  $f ( x ) = - 4 ^ { - x }$ 
D)  $f ( x ) = 4 ^ { x }$ 
A)  $f ( x ) = - 4 ^ { x }$ 
B)  $f ( x ) = 4 ^ { - x }$ 
C)  $f ( x ) = - 4 ^ { - x }$ 
D)  $f ( x ) = 4 ^ { x }$

Question 10

Find the exact value of the logarithmic expression.
-$\ln 1$

Accepted Answer

A)  1 
B)  $\mathrm { e }$ 
C)  $- 1$ 
D)  0 
A)  1 
B)  $\mathrm { e }$ 
C)  $- 1$ 
D)  0

Question 11

Change the exponential expression to an equivalent expression involving a logarithm.
-$2.3 ^ { x + 5 } = 15$

Accepted Answer

A)  $\log _ { ( x + 5 ) } 15 = 2.3$ 
B)  $\log _ { 15 } ( x + 5 ) = 2.3$ 
C)  $\log _ { 2.3 } 15 = x + 5$ 
D)  $\log _ { 2.3 } x = 10$ 
A)  $\log _ { ( x + 5 ) } 15 = 2.3$ 
B)  $\log _ { 15 } ( x + 5 ) = 2.3$ 
C)  $\log _ { 2.3 } 15 = x + 5$ 
D)  $\log _ { 2.3 } x = 10$

Question 12

Write the word or phrase that best completes each statement or answers the question.
-At a recent Phish rock concert, sound intensity reached a level of 0.50 watt per square meter. To the nearest
whole number, calculate the loudness of this sound in decibels.

Accepted Answer

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

Question 13

Choose the one alternative that best completes the statement or answers the question.
-The amount of a certain drug in the bloodstream is modeled by the function $\mathrm { y } = \mathrm { y } _ { 0 } \mathrm { e } ^ { - 0.40 \mathrm { t } }$, where $\mathrm { y } _ { 0 }$ is the amount of the drug injected (in milligrams) and $t$ is the elapsed time (in hours). Suppose that 10 milligrams are injected at 10:00 A.M. If a second injection is to be administered when there is 1 milligram of the drug present in the bloodstream, approximately when should the next dose be given? Express your answer to the nearest quarter hour.

Accepted Answer

A)  5:45 P.M 
B)  $5 : 30$ P.M 
C)  $3 : 45$ P.M 
D)  $12 : 30$ P.M 
A)  5:45 P.M 
B)  $5 : 30$ P.M 
C)  $3 : 45$ P.M 
D)  $12 : 30$ P.M

Question 14

Choose the one alternative that best completes the statement or answers the question.
Indicate whether the function is one-to-one.
-{(7, -3), (3, -7), (-2, 9), (2, -9)}

Accepted Answer

A)  No 
B)  Yes 
A)  No 
B)  Yes

Question 15

Write the word or phrase that best completes each statement or answers the question.
-How long does it take $1700 to double if it is invested at 5% interest, compounded monthly? Round your
answer to the nearest tenth.

Accepted Answer

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

Question 16

Solve the equation.
-$$\left( \frac { 7 } { 6 } \right) ^ { x } = \frac { 36 } { 49 }$$

Accepted Answer

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

Question 17

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-Which of the two rates would yield the larger amount in 1 year: $9 \%$ compounded monthly or $9 \frac { 1 } { 4 } \%$ compounded annually?

Accepted Answer

A)  $9 \%$ compounded monthly 
B)  $9 \frac { 1 } { 4 } \%$ compounded annually 
C)  They will yield the same amount. 
A)  $9 \%$ compounded monthly 
B)  $9 \frac { 1 } { 4 } \%$ compounded annually 
C)  They will yield the same amount.

Question 18

Find the exact value of the logarithmic expression.
-$\log _ { 4 } \frac { 1 } { 64 }$

Accepted Answer

A)  $- \frac { 1 } { 3 }$ 
B)  3 
C)  $\frac { 1 } { 3 }$ 
D)  $- 3$ 
A)  $- \frac { 1 } { 3 }$ 
B)  3 
C)  $\frac { 1 } { 3 }$ 
D)  $- 3$

Question 19

Write the word or phrase that best completes each statement or answers the question.
-Carla has just inherited a building that is worth $250,000. The building is in a high demand area, and the value
of the building is projected to increase at a rate of 25% per year for the next 4 years. How much more money
will she make if she waits four years to sell the building instead of selling now?

Accepted Answer

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

Question 20

Choose the one alternative that best completes the statement or answers the question.
-Sandy manages a ceramics shop and uses a $650 ^ { \circ } \mathrm { F }$ kiln to fire ceramic greenware. After turning off her kiln, she must wait until its temperature gauge reaches $205 ^ { \circ } \mathrm { F }$ before opening it and removing the ceramic pieces. If room temperature is $70 ^ { \circ } \mathrm { F }$ and the gauge reads $500 ^ { \circ } \mathrm { F }$ in 8 minutes, how long must she wait before opening the kiln? Assume the kiln cools according to Newton's Law of Cooling:
$$\mathrm { U } = \mathrm { T } + \left( \mathrm { U } _ { \mathrm { O } } - \mathrm { T } \right) \mathrm { e } ^ { \mathrm { kt } } .$$
(Round your answer to the nearest whole minute.)

Accepted Answer

A)  79 minutes 
B)  56 minutes 
C)  30 minutes 
D)  39 minutes 
A)  79 minutes 
B)  56 minutes 
C)  30 minutes 
D)  39 minutes

Solve the equation. - $8 ^ { x - 3 } = 64 ^ { 4 x }$

For the given functions f and g, find the requested composite function value. - $f ( x ) = \left| 20 x ^ { 2 } - 4 x \right| , \quad g ( x ) = 12 x - 4 ; \quad$ Find $( f \circ g ) ( 4 )$ .

Find the domain of the function. - $f ( x ) = \ln ( - 4 - x )$

Solve the problem. -An airline charter service charges a fare per person of $350 plus $20 for each unsold seat. The airplane holds 125 passengers. Let x represent the number of unsold seats and write an expression for the total revenue R for a Charter flight.

Find the inverse of the function and state its domain and range . - $\{ ( - 5 , - 3 ) , ( 3,5 ) , ( 1,1 ) , ( - 1 , - 1 ) \}$

Approximate the value using a calculator. Express answer rounded to three decimal places. - $3 ^ { 3.3 }$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\log _ { 20 } \left( x ^ { 2 } - x \right) = 1$

The graph of an exponential function is given. Match the graph to one of the following functions. -

Find the exact value of the logarithmic expression. - $\ln 1$

Change the exponential expression to an equivalent expression involving a logarithm. - $2.3 ^ { x + 5 } = 15$

Write the word or phrase that best completes each statement or answers the question. -At a recent Phish rock concert, sound intensity reached a level of 0.50 watt per square meter. To the nearest whole number, calculate the loudness of this sound in decibels.

Choose the one alternative that best completes the statement or answers the question. Indicate whether the function is one-to-one. -{(7, -3), (3, -7), (-2, 9), (2, -9)}

Write the word or phrase that best completes each statement or answers the question. -How long does it take $1700 to double if it is invested at 5% interest, compounded monthly? Round your answer to the nearest tenth.

Solve the equation. - $\left( \frac { 7 } { 6 } \right) ^ { x } = \frac { 36 } { 49 }$

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Which of the two rates would yield the larger amount in 1 year: $9 \%$ compounded monthly or $9 \frac { 1 } { 4 } \%$ compounded annually?

Find the exact value of the logarithmic expression. - $\log _ { 4 } \frac { 1 } { 64 }$

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. - 8x−3=644x8 ^ { x - 3 } = 64 ^ { 4 x }8x−3=644x

For the given functions f and g, find the requested composite function value. - f(x)=∣20x2−4x∣,g(x)=12x−4;f ( x ) = \left| 20 x ^ { 2 } - 4 x \right| , \quad g ( x ) = 12 x - 4 ; \quadf(x)=​20x2−4x​,g(x)=12x−4; Find (f∘g)(4)( f \circ g ) ( 4 )(f∘g)(4) .

Find the domain of the function. - f(x)=ln⁡(−4−x)f ( x ) = \ln ( - 4 - x )f(x)=ln(−4−x)

Solve the problem. -An airline charter service charges a fare per person of $350 plus $20 for each unsold seat. The airplane holds 125 passengers. Let x represent the number of unsold seats and write an expression for the total revenue R for a Charter flight.

Find the inverse of the function and state its domain and range . - {(−5,−3),(3,5),(1,1),(−1,−1)}\{ ( - 5 , - 3 ) , ( 3,5 ) , ( 1,1 ) , ( - 1 , - 1 ) \}{(−5,−3),(3,5),(1,1),(−1,−1)}

Approximate the value using a calculator. Express answer rounded to three decimal places. - 33.33 ^ { 3.3 }33.3

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - log⁡20(x2−x)=1\log _ { 20 } \left( x ^ { 2 } - x \right) = 1log20​(x2−x)=1

Choose the one alternative that best completes the statement or answers the question. Graph the function using a graphing utility and the Change-of-Base Formula. - log⁡x−5(x+5)\log _{x}-5(x+5)logx​−5(x+5)

The graph of an exponential function is given. Match the graph to one of the following functions. -

Find the exact value of the logarithmic expression. - ln⁡1\ln 1ln1

Change the exponential expression to an equivalent expression involving a logarithm. - 2.3x+5=152.3 ^ { x + 5 } = 152.3x+5=15

Write the word or phrase that best completes each statement or answers the question. -At a recent Phish rock concert, sound intensity reached a level of 0.50 watt per square meter. To the nearest whole number, calculate the loudness of this sound in decibels.

Choose the one alternative that best completes the statement or answers the question. Indicate whether the function is one-to-one. -{(7, -3), (3, -7), (-2, 9), (2, -9)}

Write the word or phrase that best completes each statement or answers the question. -How long does it take $1700 to double if it is invested at 5% interest, compounded monthly? Round your answer to the nearest tenth.

Solve the equation. - (76)x=3649\left( \frac { 7 } { 6 } \right) ^ { x } = \frac { 36 } { 49 }(67​)x=4936​

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Which of the two rates would yield the larger amount in 1 year: 9%9 \%9% compounded monthly or 914%9 \frac { 1 } { 4 } \%941​% compounded annually?

Find the exact value of the logarithmic expression. - log⁡4164\log _ { 4 } \frac { 1 } { 64 }log4​641​

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. - $8 ^ { x - 3 } = 64 ^ { 4 x }$

For the given functions f and g, find the requested composite function value. - $f ( x ) = \left| 20 x ^ { 2 } - 4 x \right| , \quad g ( x ) = 12 x - 4 ; \quad$ Find $( f \circ g ) ( 4 )$ .

Find the domain of the function. - $f ( x ) = \ln ( - 4 - x )$

Find the inverse of the function and state its domain and range . - $\{ ( - 5 , - 3 ) , ( 3,5 ) , ( 1,1 ) , ( - 1 , - 1 ) \}$

Approximate the value using a calculator. Express answer rounded to three decimal places. - $3 ^ { 3.3 }$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\log _ { 20 } \left( x ^ { 2 } - x \right) = 1$

Find the exact value of the logarithmic expression. - $\ln 1$

Change the exponential expression to an equivalent expression involving a logarithm. - $2.3 ^ { x + 5 } = 15$

Solve the equation. - $\left( \frac { 7 } { 6 } \right) ^ { x } = \frac { 36 } { 49 }$

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Which of the two rates would yield the larger amount in 1 year: $9 \%$ compounded monthly or $9 \frac { 1 } { 4 } \%$ compounded annually?

Find the exact value of the logarithmic expression. - $\log _ { 4 } \frac { 1 } { 64 }$