Question 1

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

Accepted Answer

A)  $\{ 3 \}$ 
B)  $\{ 4 \}$ 
C)  $\{ 16 \}$ 
D)  $\{ 2 \}$ 
A)  $\{ 3 \}$ 
B)  $\{ 4 \}$ 
C)  $\{ 16 \}$ 
D)  $\{ 2 \}$

Question 2

Change the exponential expression to an equivalent expression involving a logarithm.
-$$6 ^ { 5 } = 7776$$

Accepted Answer

A)  $\log _ { 7776 } 6 = 5$ 
B)  $\log _ { 6 } 7776 = 5$ 
C)  $\log _ { 1 / 5 } 7776 = 6$ 
D)  $\log _ { 5 } 7776 = 6$ 
A)  $\log _ { 7776 } 6 = 5$ 
B)  $\log _ { 6 } 7776 = 5$ 
C)  $\log _ { 1 / 5 } 7776 = 6$ 
D)  $\log _ { 5 } 7776 = 6$

Question 3

Determine whether the given function is exponential or not. If it is exponential, identify the value of the base a.
-$\begin{array}{cc}
\hline \mathrm{x} & \mathrm{H}(\mathrm{x}) \
\hline-1 & \frac{5}{8} \
0 & 1 \
1 & \frac{8}{5} \
2 & \frac{64}{25} \
3 & \frac{512}{125} \
\hline
\end{array}$

Accepted Answer

A)  Exponential; $a = \frac { 5 } { 8 }$ 
B)  Exponential; $a = 8$ 
C)  Exponential; $a = \frac { 8 } { 5 }$ 
D)  Not exponential 
A)  Exponential; $a = \frac { 5 } { 8 }$ 
B)  Exponential; $a = 8$ 
C)  Exponential; $a = \frac { 8 } { 5 }$ 
D)  Not exponential

Question 4

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-The formula D = 8e-0.04h can be used to find the number of milligrams D of a certain drug in a patient's bloodstream h hours after the drug has been given. When the number of milligrams reaches 4, the drug is to be
Given again. What is the time between injections?

Accepted Answer

A)  34.66 hrs 
B)  17.33 hrs 
C)  51.99 hrs 
D)  20.47 hrs 
A)  34.66 hrs 
B)  17.33 hrs 
C)  51.99 hrs 
D)  20.47 hrs

Question 5

Change the logarithmic expression to an equivalent expression involving an exponent.
-$$\log _ { \sqrt { 3 } } 64 = \frac { 7 } { 11 }$$

Accepted Answer

A)  $\sqrt { 3 } ^ { 7 / 11 } = 64$ 
B)  $\left( \frac { 7 } { 11 } \right) ^ { \sqrt { 3 } } = 64$ 
C)  $64 ^ { 7 / 11 } = \sqrt { 3 }$ 
D)  $\sqrt { 3 } ^ { 11 / 7 } = 64$ 
A)  $\sqrt { 3 } ^ { 7 / 11 } = 64$ 
B)  $\left( \frac { 7 } { 11 } \right) ^ { \sqrt { 3 } } = 64$ 
C)  $64 ^ { 7 / 11 } = \sqrt { 3 }$ 
D)  $\sqrt { 3 } ^ { 11 / 7 } = 64$

Question 6

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-A local bank advertises that it pays interest on savings accounts at the rate of 3% compounded monthly. Find the effective rate. Round answer to two decimal places.

Accepted Answer

A)  3.04% 
B)  36% 
C)  3.40% 
D)  3.44% 
A)  3.04% 
B)  36% 
C)  3.40% 
D)  3.44%

Question 7

Write the word or phrase that best completes each statement or answers the question.
-If a single pane of glass obliterates 15% of the light passing through it, then the percent P of light that passes through n
successive panes can be approximated by the equation $$P = 100 e ^ { - 0.15 n }$$ How many panes are necessary to block at least 50% of the light?

Accepted Answer

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

Question 8

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places.
-$\log _ { 3 } 25$

Accepted Answer

A)  $0.34$ 
B)  $2.93$ 
C)  $1.10$ 
D)  $3.22$ 
A)  $0.34$ 
B)  $2.93$ 
C)  $1.10$ 
D)  $3.22$

Question 9

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places.
-$\log _ { \sqrt { 3 } } 96.4$

Accepted Answer

A)  $0.120$ 
B)  $8.317$ 
C)  $4.158$ 
D)  $0.239$ 
A)  $0.120$ 
B)  $8.317$ 
C)  $4.158$ 
D)  $0.239$

Question 10

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve.
-$f(x)=x^{3}+4$

Accepted Answer

A) 
  
B) 
  
A) 
  
B)

Question 11

Solve the equation.
-$$3 ^ { 6 - 3 x } = \frac { 1 } { 27 }$$

Accepted Answer

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

Question 12

Find a formula for the inverse of the function described below.
-A size 4 dress in Country $C$ is size 42 in Country D. A function that converts dress sizes in Country $C$ to those in Country $D$ is $f ( x ) = x + 38$.

Accepted Answer

A)  $f ^ { - 1 } ( x ) = x - 38$ 
B)  $f ^ { - 1 } ( x ) = \frac { x } { - 38 }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } + 38$ 
D)  $f ^ { - 1 } ( x ) = \frac { x } { 38 }$ 
A)  $f ^ { - 1 } ( x ) = x - 38$ 
B)  $f ^ { - 1 } ( x ) = \frac { x } { - 38 }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } + 38$ 
D)  $f ^ { - 1 } ( x ) = \frac { x } { 38 }$

Question 13

Solve the exponential equation. Express the solution set in terms of natural logarithms.
-$$e ^ { x + 3 } = 6$$

Accepted Answer

A)  $\{ \ln 9 \}$ 
B)  $\{ \ln 6 - 3 \}$ 
C)  $\left\{ \mathrm { e } ^ { 18 } \right\}$ 
D)  $\left\{ e ^ { 6 } + 3 \right\}$ 
A)  $\{ \ln 9 \}$ 
B)  $\{ \ln 6 - 3 \}$ 
C)  $\left\{ \mathrm { e } ^ { 18 } \right\}$ 
D)  $\left\{ e ^ { 6 } + 3 \right\}$

Question 14

Choose the one alternative that best completes the statement or answers the question.
-The logistic growth model $\mathrm { P } ( \mathrm { t } ) = \frac { 1,450 } { 1 + 28 \mathrm { e } ^ { - 0.313 \mathrm { t } } }$ represents the population of a bacterium in a culture tube after $\mathrm { t }$ hours. What was the initial amount of bacteria in the population?

Accepted Answer

A)  55 
B)  50 
C)  49 
D)  51 
A)  55 
B)  50 
C)  49 
D)  51

Question 15

Change the exponential expression to an equivalent expression involving a logarithm.
-$$5 ^ { 2 } = 25$$

Accepted Answer

A)  $\log _ { 2 } 25 = 5$ 
B)  $\log _ { 5 } 2 = 25$ 
C)  $\log _ { 25 } 5 = 2$ 
D)  $\log _ { 5 } 25 = 2$ 
A)  $\log _ { 2 } 25 = 5$ 
B)  $\log _ { 5 } 2 = 25$ 
C)  $\log _ { 25 } 5 = 2$ 
D)  $\log _ { 5 } 25 = 2$

Question 16

Find functions f and g so that f ° g = H.
-$$H ( x ) = | 3 x + 7 |$$

Accepted Answer

A)  $f ( x ) = x ; g ( x ) = 3 x + 7$ 
B)  $f ( x ) = | x |$;
$g ( x ) = 3 x + 7$ 
C)  $f ( x ) = | - x | ; \quad g ( x ) = 3 x - 7$ 
D)  $f ( x ) = - | x | ; \quad g ( x ) = 3 x + 7$ 
A)  $f ( x ) = x ; g ( x ) = 3 x + 7$ 
B)  $f ( x ) = | x |$;
$g ( x ) = 3 x + 7$ 
C)  $f ( x ) = | - x | ; \quad g ( x ) = 3 x - 7$ 
D)  $f ( x ) = - | x | ; \quad g ( x ) = 3 x + 7$

Question 17

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-Between 7:00 AM and 8:00 AM, trains arrive at a subway station at a rate of 15 trains per hour (0.25 trains per minute). The following formula from statistics can be used to determine the probability that a train will arrive within t
Minutes of 7:00 AM. $$F ( t ) = 1 - e ^ { - 0.25 t }$$ Determine how many minutes are needed for the probability to reach 20%.

Accepted Answer

A)  $0.89 \mathrm {~min}$ 
B)  $2.35 \mathrm {~min}$ 
C)  $5.34 \mathrm {~min}$ 
D)  $4.12 \mathrm {~min}$ 
A)  $0.89 \mathrm {~min}$ 
B)  $2.35 \mathrm {~min}$ 
C)  $5.34 \mathrm {~min}$ 
D)  $4.12 \mathrm {~min}$

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

Change the exponential expression to an equivalent expression involving a logarithm. - $6 ^ { 5 } = 7776$

Determine whether the given function is exponential or not. If it is exponential, identify the value of the base a. - () -1 0 1 1 2 3

Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { \sqrt { 3 } } 64 = \frac { 7 } { 11 }$

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -A local bank advertises that it pays interest on savings accounts at the rate of 3% compounded monthly. Find the effective rate. Round answer to two decimal places.

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - $\log _ { 3 } 25$

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places. - $\log _ { \sqrt { 3 } } 96.4$

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve. - $f(x)=x^{3}+4$ $The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve. - f(x)=x^{3}+4$

Solve the equation. - $3 ^ { 6 - 3 x } = \frac { 1 } { 27 }$

Find a formula for the inverse of the function described below. -A size 4 dress in Country $C$ is size 42 in Country D. A function that converts dress sizes in Country $C$ to those in Country $D$ is $f ( x ) = x + 38$ .

Solve the exponential equation. Express the solution set in terms of natural logarithms. - $e ^ { x + 3 } = 6$

Change the exponential expression to an equivalent expression involving a logarithm. - $5 ^ { 2 } = 25$

Find functions f and g so that f ° g = H. - $H ( x ) = | 3 x + 7 |$

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. - 4x=644 ^ { x } = 644x=64

Change the exponential expression to an equivalent expression involving a logarithm. - 65=77766 ^ { 5 } = 777665=7776