Question 1

Solve the problem.
-Suppose that $f ( x ) = 3 ^ { x } + 1$. If $f ( x ) = 1 / 244$, what is $x$ ?

Accepted Answer

A)  5 
B)  1 
C)  $- 1$ 
D)  $- 5$ 
A)  5 
B)  1 
C)  $- 1$ 
D)  $- 5$

Question 2

Solve the problem.
-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 3

Solve the problem.
-How much money needs to be invested now to get $2000 after 4 years at 8% compounded quarterly? Express your answer to the nearest dollar.

Accepted Answer

A)  $2746 
B)  $1848 
C)  $1457 
D)  $584 
A)  $2746 
B)  $1848 
C)  $1457 
D)  $584

Question 4

Solve the problem.
-An oil well off the Gulf Coast is leaking, with the leak spreading oil over the surface of the gulf as a circle. At any time t, in minutes, after the beginning of the leak, the radius of the oil slick on the surface is r(t) = 3t ft. Find
The area A of the oil slick as a function of time. A) $\mathrm { A } ( \mathrm { r } ( \mathrm { t } ) ) = 9 \pi \mathrm { t } ^ { 2 }$

Accepted Answer

B)  $A ( r ( t ) ) = 9 t ^ { 2 }$ 
C)  $\mathrm { A } ( \mathrm { r } ( \mathrm { t } ) ) = 9 \pi \mathrm { t }$ 
D)  $\mathrm { A } ( \mathrm { r } ( \mathrm { t } ) ) = 3 \pi \mathrm { t } ^ { 2 }$ 
B)  $A ( r ( t ) ) = 9 t ^ { 2 }$ 
C)  $\mathrm { A } ( \mathrm { r } ( \mathrm { t } ) ) = 9 \pi \mathrm { t }$ 
D)  $\mathrm { A } ( \mathrm { r } ( \mathrm { t } ) ) = 3 \pi \mathrm { t } ^ { 2 }$

Question 5

Change the logarithmic expression to an equivalent expression involving an exponent.
-$\ln y = 8$

Accepted Answer

A)  $e ^ { 8 } = y$ 
B)  $y ^ { 8 } = e$ 
C)  $e ^ { y } = 8$ 
D)  $8 ^ { \mathrm { e } } = \mathrm { y }$ 
A)  $e ^ { 8 } = y$ 
B)  $y ^ { 8 } = e$ 
C)  $e ^ { y } = 8$ 
D)  $8 ^ { \mathrm { e } } = \mathrm { y }$

Question 6

Change the logarithmic expression to an equivalent expression involving an exponent.
-$\log _ { \mathrm { b } } 81 = 4$

Accepted Answer

A)  $81 ^ { b } = 4$ 
B)  $81 ^ { 4 } = b$ 
C)  $b ^ { 4 } = 81$ 
D)  $4 ^ { b } = 81$ 
A)  $81 ^ { b } = 4$ 
B)  $81 ^ { 4 } = b$ 
C)  $b ^ { 4 } = 81$ 
D)  $4 ^ { b } = 81$

Question 7

Solve the equation.
-$$e ^ { 6 x - 1 } = \left( e ^ { 4 } \right) ^ { - x }$$

Accepted Answer

A)  $\{ 0 \}$ 
B)  $\left\{ \frac { 5 } { 7 } \right\}$ 
C)  $\left\{ \frac { 1 } { 10 } \right\}$ 
D)  $\left\{ \frac { 1 } { 2 } \right\}$ 
A)  $\{ 0 \}$ 
B)  $\left\{ \frac { 5 } { 7 } \right\}$ 
C)  $\left\{ \frac { 1 } { 10 } \right\}$ 
D)  $\left\{ \frac { 1 } { 2 } \right\}$

Question 8

Find the present value. Round to the nearest cent.
-To get $5600 after 8 years at 5% compounded annually

Accepted Answer

A)  $3,639.62 
B)  $2,260.9 
C)  $5,962.67 
D)  $3790.30 
A)  $3,639.62 
B)  $2,260.9 
C)  $5,962.67 
D)  $3790.30

Question 9

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) $\begin{array}{l}
f(x): D=\{x \mid x \leq 0\}, R=\{y|y \leq 0\rangle \
f^{-1}(x): D=\left\{x|x \leq 0\rangle, R=\left\{y \mid y \leq-\frac{5}{4}\right\}\right.
\end{array}$ 
B) $\begin{array}{l}
f(x): D=\left\{x \mid x \geq-\frac{5}{4}\right\}, R=\{y \mid y \geq 0\} \
\mathrm{f}^{-1}(\mathrm{x}) \text { : D is all real numbers, } \mathrm{R}=\left\{y \mid \mathrm{y} \geq-\frac{5}{4}\right\}
\end{array}$ 
C) $\begin{array}{l}
f(x): D=\left\{x \mid x \geq-\frac{5}{4}\right\}, R=\{y \mid y \geq 0\} \
f^{-1}(x): D=\{x \mid x \geq 0\}, R=\left\{y \mid y \geq-\frac{5}{4}\right\}
\end{array}$ 
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) $\begin{array}{l}
f(x): D=\{x \mid x \leq 0\}, R=\{y|y \leq 0\rangle \
f^{-1}(x): D=\left\{x|x \leq 0\rangle, R=\left\{y \mid y \leq-\frac{5}{4}\right\}\right.
\end{array}$ 
B) $\begin{array}{l}
f(x): D=\left\{x \mid x \geq-\frac{5}{4}\right\}, R=\{y \mid y \geq 0\} \
\mathrm{f}^{-1}(\mathrm{x}) \text { : D is all real numbers, } \mathrm{R}=\left\{y \mid \mathrm{y} \geq-\frac{5}{4}\right\}
\end{array}$ 
C) $\begin{array}{l}
f(x): D=\left\{x \mid x \geq-\frac{5}{4}\right\}, R=\{y \mid y \geq 0\} \
f^{-1}(x): D=\{x \mid x \geq 0\}, R=\left\{y \mid y \geq-\frac{5}{4}\right\}
\end{array}$ 
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 10

Solve the problem.
-A venture capital firm invested $2,000,000 in a new company in 1995. In 1999, they sold their stake in the
company for $10,500,000. What was the average annual rate of return on their investment?

Accepted Answer

The answer of Solve the problem.
-A venture capital firm invested...

Question 11

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 12

Find the amount that results from the investment.
-$1,000 invested at 6% compounded annually after a period of 8 years

Accepted Answer

A)  $1,503.63 
B)  $593.85 
C)  $1,689.48 
D)  $1,593.85 
A)  $1,503.63 
B)  $593.85 
C)  $1,689.48 
D)  $1,593.85

Question 13

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

Accepted Answer

B)

C) 
  
D) 
  
B)

C) 
  
D)

Question 14

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

Accepted Answer

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

Question 15

Solve the problem.
-If $3 ^ { - x } = \frac { 1 } { 5 }$, what does $9 ^ { x }$ equal?

Accepted Answer

A)  $- 25$ 
B)  5 
C)  25 
D)  $\frac { 1 } { 25 }$ 
A)  $- 25$ 
B)  5 
C)  25 
D)  $\frac { 1 } { 25 }$

Question 16

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places.
-$\log _ { 4.4 } 2.6$

Accepted Answer

A)  $0.645$ 
B)  0.591 
C)  1.551 
D)  0.415 
A)  $0.645$ 
B)  0.591 
C)  1.551 
D)  0.415

Question 17

Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function.
-$f(x)=-2^{x+3}+4$
 
 A) domain of $f : ( - \infty , \infty )$; range of $f : ( - \infty , - 4 )$;
horizontal asymptote: $\mathrm { y } = - 4$

Accepted Answer

B)  domain of $\mathrm { f } : ( - \infty , \infty )$; range of $\mathrm { f } : ( - \infty , - 4 )$; 
horizontal asymptote: $\mathrm { y } = - 4$

C)  domain of $\mathrm { f: } ( - \infty , \infty )$; range of $\mathrm { f } : ( - 4 , \infty )$;
horizontal asymptote: $\mathrm { y } = 4$

D)  domain of $f : ( - \infty , \infty )$; range of $f : ( - \infty , 4 )$;
 horizontal asymptote: $y = 4$ 
  
B)  domain of $\mathrm { f } : ( - \infty , \infty )$; range of $\mathrm { f } : ( - \infty , - 4 )$; 
horizontal asymptote: $\mathrm { y } = - 4$

C)  domain of $\mathrm { f: } ( - \infty , \infty )$; range of $\mathrm { f } : ( - 4 , \infty )$;
horizontal asymptote: $\mathrm { y } = 4$

D)  domain of $f : ( - \infty , \infty )$; range of $f : ( - \infty , 4 )$;
 horizontal asymptote: $y = 4$

Question 18

The Richter scale converts seismographic readings into numbers for measuring the magnitude of an earthquake according to this
function $$M ( x ) = \log \left( \frac { x } { x _ { 0 } } \right) , \text { where } x _ { 0 } = 10 ^ { - 3 }$$
-What is the magnitude of an earthquake whose seismographic reading is 6.6 millimeters at a distance of 100 kilometers from its epicenter? Round the answer to the nearest tenth.

Accepted Answer

A)  2.8 
B)  3.8 
C)  2.5 
D)  819.5 
A)  2.8 
B)  3.8 
C)  2.5 
D)  819.5

Question 19

Find the domain of the composite function f $f ^ { \circ } g $
-$$f ( x ) = \frac { - 2 } { x + 7 } ; \quad g ( x ) = \frac { - 14 } { x }$$

Accepted Answer

A)  $\{ x \mid x \neq 0 , x \neq - 7 , x \neq 2 \}$ 
B)  $\{ x \mid x$ is any real number $\}$ 
C)  $\{ x \mid x \neq 0 , x \neq - 7 \}$ 
D)  $\{ x \mid x \neq 0 , x \neq 2 \}$ 
A)  $\{ x \mid x \neq 0 , x \neq - 7 , x \neq 2 \}$ 
B)  $\{ x \mid x$ is any real number $\}$ 
C)  $\{ x \mid x \neq 0 , x \neq - 7 \}$ 
D)  $\{ x \mid x \neq 0 , x \neq 2 \}$

Question 20

Find the domain of the function.
-$$f ( x ) = \log _ { 4 } ( x - 9 ) ^ { 2 }$$

Accepted Answer

A)  $( - \infty , 9 )$ or $( 9 , \infty )$ 
B)  $( 9 , \infty )$ 
C)  $( - \infty , 0 )$ or $( 0 , \infty )$ 
D)  $( - 9 , \infty )$ 
A)  $( - \infty , 9 )$ or $( 9 , \infty )$ 
B)  $( 9 , \infty )$ 
C)  $( - \infty , 0 )$ or $( 0 , \infty )$ 
D)  $( - 9 , \infty )$

Solve the problem. -Suppose that $f ( x ) = 3 ^ { x } + 1$ . If $f ( x ) = 1 / 244$ , what is $x$ ?

Solve the problem. -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.)

Solve the problem. -How much money needs to be invested now to get $2000 after 4 years at 8% compounded quarterly? Express your answer to the nearest dollar.

Change the logarithmic expression to an equivalent expression involving an exponent. - $\ln y = 8$

Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { \mathrm { b } } 81 = 4$

Solve the equation. - $e ^ { 6 x - 1 } = \left( e ^ { 4 } \right) ^ { - x }$

Find the present value. Round to the nearest cent. -To get $5600 after 8 years at 5% compounded annually

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. - $f ( x ) = \sqrt { 5 + 4 x }$

Solve the problem. -A venture capital firm invested $2,000,000 in a new company in 1995. In 1999, they sold their stake in the company for $10,500,000. What was the average annual rate of return on their investment?

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

Find the amount that results from the investment. -$1,000 invested at 6% compounded annually after a period of 8 years

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

Solve the problem. -If $3 ^ { - x } = \frac { 1 } { 5 }$ , what does $9 ^ { x }$ equal?

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places. - $\log _ { 4.4 } 2.6$

Find the domain of the composite function f $f ^ { \circ } g$ - $f ( x ) = \frac { - 2 } { x + 7 } ; \quad g ( x ) = \frac { - 14 } { x }$

Find the domain of the function. - $f ( x ) = \log _ { 4 } ( x - 9 ) ^ { 2 }$

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

Review

Filters

Exam 4: Exponential and Logarithmic Functions

Solve the problem. -Suppose that f(x)=3x+1f ( x ) = 3 ^ { x } + 1f(x)=3x+1 . If f(x)=1/244f ( x ) = 1 / 244f(x)=1/244 , what is xxx ?