Question 1

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

Question 2

Write the word or phrase that best completes each statement or answers the question.
-The bacteria in a container quadruples every day. If there are initially 100 bacteria, write an equation that
models the number of bacteria A after d days. How many bacteria will there be after 1 week?

Accepted Answer

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

Question 3

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$$e ^ { x + 8 } = 4$$

Accepted Answer

A)  $\left\{ e ^ { 4 } + 8 \right\}$ 
B)  $\left\{ \mathrm { e } ^ { 32 } \right\}$ 
C)  $\{ \ln 12 \}$ 
D)  $\{ \ln 4 - 8 \}$ 
A)  $\left\{ e ^ { 4 } + 8 \right\}$ 
B)  $\left\{ \mathrm { e } ^ { 32 } \right\}$ 
C)  $\{ \ln 12 \}$ 
D)  $\{ \ln 4 - 8 \}$

Question 4

Solve the problem. Round your answer to three decimals.
-What annual rate of interest is required to triple an investment in 7 years?

Accepted Answer

A)  10.409% 
B)  16.993% 
C)  8.497% 
D)  15.694% 
A)  10.409% 
B)  16.993% 
C)  8.497% 
D)  15.694%

Question 5

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$$e ^ { 3 x } = 5$$

Accepted Answer

A)  $\left\{ \frac { \ln 3 } { 5 } \right\}$ 
B)  $\{ 3 \ln 5 \}$ 
C)  $\left\{ \frac { \ln 5 } { 3 } \right\}$ 
D)  $\left\{ \frac { 5 } { 3 } e \right\}$ 
A)  $\left\{ \frac { \ln 3 } { 5 } \right\}$ 
B)  $\{ 3 \ln 5 \}$ 
C)  $\left\{ \frac { \ln 5 } { 3 } \right\}$ 
D)  $\left\{ \frac { 5 } { 3 } e \right\}$

Question 6

Find the exact value of the logarithmic expression.
-$\log _ { 5 } \frac { 1 } { 25 }$

Accepted Answer

A)  2 
B)  $- 2$ 
C)  5 
D)  $- 5$ 
A)  2 
B)  $- 2$ 
C)  5 
D)  $- 5$

Question 7

Solve the problem.
-The function $\mathrm { f } ( \mathrm { x } ) = 1 + 1.5 \ln ( \mathrm { x } + 1 )$ 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 13 days of practice, what is the average number of consecutive free throws the basketball player makes?

Accepted Answer

A)  8 consecutive free throws 
B)  6 consecutive free throws 
C)  9 consecutive free throws 
D)  5 consecutive free throws 
A)  8 consecutive free throws 
B)  6 consecutive free throws 
C)  9 consecutive free throws 
D)  5 consecutive free throws

Question 8

Choose the one alternative that best completes the statement or answers the question.
-The logistic growth function $\mathrm { f } ( \mathrm { t } ) = \frac { 440 } { 1 + 7.8 \mathrm { e } ^ { - 0.17 \mathrm { t } } }$ describes the population of a species of butterflies $\mathrm { t }$ 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 
A)  2 butterflies 
B)  50 butterflies 
C)  8 butterflies 
D)  440 butterflies

Question 9

Graph the function.
-$$f ( x ) = e ^ { 2 x }$$

Accepted Answer

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

Question 10

For the given functions f and g, find the requested composite function value.
-$f ( x ) = \frac { x - 6 } { x } , g ( x ) = x ^ { 2 } + 9 ; \quad$ Find $( g \circ f ) ( - 2 )$

Accepted Answer

A)  $\frac { 7 } { 13 }$ 
B)  13 
C)  $\frac { 145 } { 16 }$ 
D)  25 
A)  $\frac { 7 } { 13 }$ 
B)  13 
C)  $\frac { 145 } { 16 }$ 
D)  25

Question 11

Solve the problem.
-Find out how long it takes a $\$ 2,700$ investment to double if it is invested at $7 \%$ compounded semiannually. Round to the nearest tenth of a year. Use the formula $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$.

Accepted Answer

A)  $9.9$ years 
B)  $10.3$ years 
C)  $10.5$ years 
D)  $10.1$ years 
A)  $9.9$ years 
B)  $10.3$ years 
C)  $10.5$ years 
D)  $10.1$ years

Question 12

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

Accepted Answer

A)  $f ( x ) = 4 ^ { x } + 1$ 
B)  $f ( x ) = 4 ^ { x }$ 
C)  $f ( x ) = 4 ^ { x } - 1$ 
D)  $f ( x ) = 4 ^ { x + 1 }$ 
A)  $f ( x ) = 4 ^ { x } + 1$ 
B)  $f ( x ) = 4 ^ { x }$ 
C)  $f ( x ) = 4 ^ { x } - 1$ 
D)  $f ( x ) = 4 ^ { x + 1 }$

Question 13

Determine i) the domain of the function, ii) the range of the function, iii) the domain of the inverse, and iv) the range of
the inverse.
-$$f ( x ) = \sqrt { 5 + 4 x }$$

Accepted Answer

A) 
$\begin{array}{l}
f(x): D=\{x \mid x \leq 0\}, R=\{y|y \leq 0\rangle \
\left\{-1(x): D=\left\{x|x \leq 0\rangle, R=\left\{y \mid y \leq-\frac{5}{4}\right\}\right.\right.
\end{array}$ 
B)  
$$
f(x): D=\left\{x \mid x \geq-\frac{5}{4}\right\}, R=\{y \mid y \geq 0\}
$$
$ \mathrm{f}^{-1}(\mathrm{x}): \mathrm{D} $ is all real numbers, $ \mathrm{R}=\left\{\mathrm{y} \mid \mathrm{y} \geq-\frac{5}{4}\right\} $ 
C) 
$\begin{array}{c}
f(x): D=\left\{x \mid x \geq-\frac{5}{4}\right\}, R=\{y \mid y \geq 0\} \
f-1(x): D=\{x \mid x \geq 0\}, R=\left\{y \mid y \geq-\frac{5}{4}\right\}
\end{array}$ 
D)  
$ f(x): D=\left\{x \mid x \geq-\frac{5}{4}\right\}, R $ is all real numbers; $ f^{-1}(x): D $ is all real numbers, $ R=\left\{y \mid y \geq-\frac{5}{4}\right\} $ 
A) 
$\begin{array}{l}
f(x): D=\{x \mid x \leq 0\}, R=\{y|y \leq 0\rangle \
\left\{-1(x): D=\left\{x|x \leq 0\rangle, R=\left\{y \mid y \leq-\frac{5}{4}\right\}\right.\right.
\end{array}$ 
B)  
$$
f(x): D=\left\{x \mid x \geq-\frac{5}{4}\right\}, R=\{y \mid y \geq 0\}
$$
$ \mathrm{f}^{-1}(\mathrm{x}): \mathrm{D} $ is all real numbers, $ \mathrm{R}=\left\{\mathrm{y} \mid \mathrm{y} \geq-\frac{5}{4}\right\} $ 
C) 
$\begin{array}{c}
f(x): D=\left\{x \mid x \geq-\frac{5}{4}\right\}, R=\{y \mid y \geq 0\} \
f-1(x): D=\{x \mid x \geq 0\}, R=\left\{y \mid y \geq-\frac{5}{4}\right\}
\end{array}$ 
D)  
$ f(x): D=\left\{x \mid x \geq-\frac{5}{4}\right\}, R $ is all real numbers; $ f^{-1}(x): D $ is all real numbers, $ R=\left\{y \mid y \geq-\frac{5}{4}\right\} $

Question 14

Solve the problem.
-The function $\mathrm { D } ( \mathrm { h } ) = 5 \mathrm { e } ^ { - 0.4 \mathrm {~h} }$ can be used to determine the milligrams $\mathrm { D }$ of a certain drug in a patient's bloodstream h hours after the drug has been given. How many milligrams (to two decimals) will be present after 11 hours?

Accepted Answer

A)  $407.25 \mathrm { mg }$ 
B)  $1.49 \mathrm { mg }$ 
C)  $3.09 \mathrm { mg }$ 
D)  $0.06 \mathrm { mg }$ 
A)  $407.25 \mathrm { mg }$ 
B)  $1.49 \mathrm { mg }$ 
C)  $3.09 \mathrm { mg }$ 
D)  $0.06 \mathrm { mg }$

Question 15

Solve the problem.
-Two bacteria are placed in a petri dish. The population will double every day. The formula for the number of bacteria in the dish on day t is $$N ( t ) = 2 ( 2 ) ^ { t }$$ where t is the number of days after the two bacteria are placed in the dish. How many bacteria are in the dish
Seven days after the two bacteria are placed in the dish?

Accepted Answer

A)  98 
B)  11 
C)  256 
D)  28 
A)  98 
B)  11 
C)  256 
D)  28

Question 16

Solve the problem.
-The population P of a predator mammal depends upon the number x of a smaller animal that is its primary food source. The population s of the smaller animal depends upon the amount a of a certain plant that is its
Primary food source. If P(x) = 3x2 + 2 and s(a) = 2a + 5, what is the relationship between the predator mammal
And the plant food source?

Accepted Answer

A)  $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 4 \mathrm { a } ^ { 2 } + 20 \mathrm { a } + 27$ 
B)  $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 6 \mathrm { a } + 7$ 
C)  $P ( s ( a ) ) = 12 a ^ { 2 } + 30 a + 77$ 
D)  $P ( s ( a ) ) = 12 a ^ { 2 } + 60 a + 77$ 
A)  $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 4 \mathrm { a } ^ { 2 } + 20 \mathrm { a } + 27$ 
B)  $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 6 \mathrm { a } + 7$ 
C)  $P ( s ( a ) ) = 12 a ^ { 2 } + 30 a + 77$ 
D)  $P ( s ( a ) ) = 12 a ^ { 2 } + 60 a + 77$

Question 17

Graph the function.
-$f(x)=e^{-0.3 x}$

Accepted Answer

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

Question 18

Choose the one alternative that best completes the statement or answers the question.
Indicate whether the function is one-to-one.
-{(6, -6), (12, -5), (10, -4), (8, -3)}

Accepted Answer

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

Question 19

Solve the equation.
-$$3 ^ { 1 + 2 x } = 27$$

Accepted Answer

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

Question 20

Choose the one alternative that best completes the statement or answers the question.
The graph of a logarithmic function is shown. Select the function which matches the graph.
-

Accepted Answer

A)  $f ( x ) = - \log _ { 3 } x$ 
B)  $f ( x ) = \log _ { 3 } x$ 
C)  $f ( x ) = 1 - \log _ { 3 } x$ 
D)  $f ( x ) = \log _ { 3 } ( - x )$ 
A)  $f ( x ) = - \log _ { 3 } x$ 
B)  $f ( x ) = \log _ { 3 } x$ 
C)  $f ( x ) = 1 - \log _ { 3 } x$ 
D)  $f ( x ) = \log _ { 3 } ( - x )$

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.

Write the word or phrase that best completes each statement or answers the question. -The bacteria in a container quadruples every day. If there are initially 100 bacteria, write an equation that models the number of bacteria A after d days. How many bacteria will there be after 1 week?

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $e ^ { x + 8 } = 4$

Solve the problem. Round your answer to three decimals. -What annual rate of interest is required to triple an investment in 7 years?

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $e ^ { 3 x } = 5$

Find the exact value of the logarithmic expression. - $\log _ { 5 } \frac { 1 } { 25 }$

Graph the function. - $f ( x ) = e ^ { 2 x }$ $Graph the function. - f ( x ) = e ^ { 2 x }$

For the given functions f and g, find the requested composite function value. - $f ( x ) = \frac { x - 6 } { x } , g ( x ) = x ^ { 2 } + 9 ; \quad$ Find $( g \circ f ) ( - 2 )$

Solve the problem. -Find out how long it takes a $\$ 2,700$ investment to double if it is invested at $7 \%$ compounded semiannually. Round to the nearest tenth of a year. Use the formula $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ .

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

Determine i) the domain of the function, ii) the range of the function, iii) the domain of the inverse, and iv) the range of the inverse. - $f ( x ) = \sqrt { 5 + 4 x }$

Graph the function. - $f(x)=e^{-0.3 x}$ $Graph the function. - f(x)=e^{-0.3 x}$

Choose the one alternative that best completes the statement or answers the question. Indicate whether the function is one-to-one. -{(6, -6), (12, -5), (10, -4), (8, -3)}

Solve the equation. - $3 ^ { 1 + 2 x } = 27$

Choose the one alternative that best completes the statement or answers the question. The graph of a logarithmic function is shown. Select the function which matches the graph. -

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