Question 1

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places.
-$\log _ { 8 } 0.537$

Accepted Answer

A)  -0.299 
B)  14.898 
C)  -3.344 
D)  -0.270 
A)  -0.299 
B)  14.898 
C)  -3.344 
D)  -0.270

Question 2

Solve the problem.
-The size P of a certain insect population at time t (in days) obeys the function $\mathrm { P } = 700 \mathrm { e } ^ { 0.03 \mathrm { t } }$ After how many
days will the population reach 1500?

Accepted Answer

The answer of Solve the problem.
-The size P of a...

Question 3

Express as a single logarithm.
-$\log _ { \mathrm { c } } \mathrm { m } + \log _ { \mathrm { c } } \mathrm { n }$

Accepted Answer

A)  $\log _ { \mathrm { C } } \mathrm { mn }$ 
B)  $\log _ { \mathrm { C } } ( \mathrm { mn } )$ 
C)  $\log _ { \mathrm { C } } \mathrm { m } \cdot \log _ { \mathrm { C } } \mathrm { n }$ 
D)  $\log _ { \mathrm { c } } \frac { \mathrm { m } } { \mathrm { n } }$ 
A)  $\log _ { \mathrm { C } } \mathrm { mn }$ 
B)  $\log _ { \mathrm { C } } ( \mathrm { mn } )$ 
C)  $\log _ { \mathrm { C } } \mathrm { m } \cdot \log _ { \mathrm { C } } \mathrm { n }$ 
D)  $\log _ { \mathrm { c } } \frac { \mathrm { m } } { \mathrm { n } }$

Question 4

Find a formula for the inverse of the function described below.
-An organization determines that the cost per person of chartering a bus is given by the formula $$C ( x ) = \frac { 200 + 6 x } { x }$$ where x is the number of people in the group and C(x) is in dollars. A) $C ^ { - 1 } ( x ) = \frac { 200 + x } { 6 }$

Accepted Answer

B)  $C ^ { - 1 } ( x ) = \frac { 6 } { x - 200 }$ 
C)  $C ^ { - 1 } ( x ) = \frac { 200 } { x + 6 }$ 
D)  $C ^ { - 1 } ( x ) = \frac { 200 } { x - 6 }$ 
B)  $C ^ { - 1 } ( x ) = \frac { 6 } { x - 200 }$ 
C)  $C ^ { - 1 } ( x ) = \frac { 200 } { x + 6 }$ 
D)  $C ^ { - 1 } ( x ) = \frac { 200 } { x - 6 }$

Question 5

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

Question 6

Find the domain of the composite function f $f ^ { \circ } g $
-$$f ( x ) = \frac { x } { x + 7 } ; \quad g ( x ) = \frac { 7 } { x + 5 }$$

Accepted Answer

A)  $\{ x \mid x \neq - 5 , x \neq - 6 \}$ 
B)  $\{ x \mid x \neq 0 , x \neq - 5 , x \neq - 6 \}$ 
C)  $\{ x \mid x$ is any real number $\}$ 
D)  $\{ x \mid x \neq - 5 , x \neq - 7 \}$ 
A)  $\{ x \mid x \neq - 5 , x \neq - 6 \}$ 
B)  $\{ x \mid x \neq 0 , x \neq - 5 , x \neq - 6 \}$ 
C)  $\{ x \mid x$ is any real number $\}$ 
D)  $\{ x \mid x \neq - 5 , x \neq - 7 \}$

Question 7

Solve the equation.
-$\ln x + \ln ( x + 4 ) = 1$

Accepted Answer

A)  $\frac { - 4 + 2 \sqrt { 16 + \mathrm { e } ^ { 1 } } } { 2 } \approx 2.326$ 
B)  $\frac { - 4 + \sqrt { 16 + 4 \mathrm { e } ^ { 1 } } } { 2 } \approx 0.592$ 
C)  $- 4 + \sqrt { 16 + 4 \mathrm { e } ^ { 1 } } \approx 1.184$ 
D)  $\frac { - 4 - \sqrt { 16 + 4 \mathrm { e } ^ { 1 } } } { 2 } \approx - 4.592$ 
A)  $\frac { - 4 + 2 \sqrt { 16 + \mathrm { e } ^ { 1 } } } { 2 } \approx 2.326$ 
B)  $\frac { - 4 + \sqrt { 16 + 4 \mathrm { e } ^ { 1 } } } { 2 } \approx 0.592$ 
C)  $- 4 + \sqrt { 16 + 4 \mathrm { e } ^ { 1 } } \approx 1.184$ 
D)  $\frac { - 4 - \sqrt { 16 + 4 \mathrm { e } ^ { 1 } } } { 2 } \approx - 4.592$

Question 8

Solve the problem.
-The population (in hundred thousands) for the Colonial United States in ten-year increments for the years
1700-1780 is given in the table. (Source: 1998 Information Please Almanac)   State whether the data can be more accurately modeled using an exponential function or a logarithmic function. Using a
graphing utility, find a model for population (in hundred thousands) as a function of decades since 1700.

Accepted Answer

The answer of Solve the problem.
-The population (in hundred thousands)...

Question 9

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

Accepted Answer

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

Question 10

Use the graph of the given one-to-one function to sketch the graph of the inverse function. For convenience, the graph of
y = x is also given.
-  A)

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

Solve the problem. Round your answer to three decimals.
-How long will it take for an investment to double in value if it earns 9.25% compounded continuously?

Accepted Answer

A)  7.493 years 
B)  3.747 years 
C)  7.781 years 
D)  11.877 years 
A)  7.493 years 
B)  3.747 years 
C)  7.781 years 
D)  11.877 years

Question 13

Solve the problem.
-A nuclear scientist has a sample of 100 mg of a radioactive material which has a half-life in hours. She monitors the amount of radioactive material over a period of a day and obtains the following data. Use a graphing utility
To fit an exponential function to the data. Predict the amount of material remaining at 40 hours. $\begin{array}{l|lcccccc}
\text { Hours } & 0 & 5 & 10 & 15 & 20 & 25 & 30 \
\hline \mathrm{mg} & 100 & 68.3 & 45.2 & 31.3 & 21.5 & 14.6 & 9.8
\end{array}$

Accepted Answer

A)  $\mathrm { y } = 92 \mathrm { e } ^ { - 0.0686 \mathrm { x } } , 5.9 \mathrm { mg }$ 
C)  $\mathrm { y } = 100 \mathrm { e } ^ { - 0.077 \mathrm { x } } , 4.6 \mathrm { mg }$ 
D)  $\mathrm { y } = 100 \mathrm { e } ^ { - 0.077 \mathrm { x } } , 6.7 \mathrm { mg }$ 
A)  $\mathrm { y } = 92 \mathrm { e } ^ { - 0.0686 \mathrm { x } } , 5.9 \mathrm { mg }$ 
C)  $\mathrm { y } = 100 \mathrm { e } ^ { - 0.077 \mathrm { x } } , 4.6 \mathrm { mg }$ 
D)  $\mathrm { y } = 100 \mathrm { e } ^ { - 0.077 \mathrm { x } } , 6.7 \mathrm { mg }$

Question 14

Solve the problem.
-Tracey bought a diamond ring appraised at $1,700 at an antique store. If diamonds have appreciated in value at an annual rate of 10%, what was the value of the ring 10 years ago? (Round your answer to the nearest dollar.)

Accepted Answer

A)  $230 
B)  $655 
C)  $625 
D)  $4,409 
A)  $230 
B)  $655 
C)  $625 
D)  $4,409

Question 15

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

Accepted Answer

A)  $\left\{ \frac { \ln 6 } { 3 } \right\}$ 
B)  $\left\{ \frac { \ln 3 } { 6 } \right\}$ 
C)  $\{ 3 \ln 6 \}$ 
D)  $\{ 2 \mathrm { e } \}$ 
A)  $\left\{ \frac { \ln 6 } { 3 } \right\}$ 
B)  $\left\{ \frac { \ln 3 } { 6 } \right\}$ 
C)  $\{ 3 \ln 6 \}$ 
D)  $\{ 2 \mathrm { e } \}$

Question 16

Approximate the value using a calculator. Express answer rounded to three decimal places.
-$\mathrm { e } ^ { - 2.7 }$

Accepted Answer

A)  0.367 
B)  0.067 
C)  -0.067 
D)  -7.339 
A)  0.367 
B)  0.067 
C)  -0.067 
D)  -7.339

Question 17

Change the exponential expression to an equivalent expression involving a logarithm.
-$$13 ^ { x } = 169$$

Accepted Answer

A)  $\log _ { 169 } 13 = x$ 
B)  $\log _ { 13 } 169 = x$ 
C)  $\log _ { 169 } x = 13$ 
D)  $\log _ { \mathrm { x } } 169 = 13$ 
A)  $\log _ { 169 } 13 = x$ 
B)  $\log _ { 13 } 169 = x$ 
C)  $\log _ { 169 } x = 13$ 
D)  $\log _ { \mathrm { x } } 169 = 13$

Question 18

Graph the function.
-$f(x)=-4 \ln x$
 
 A)

Accepted Answer

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

Question 19

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places.
-$\log _ { 6,9 } 2.8$

Accepted Answer

A)  0.41 
B)  0.53 
C)  0.45 
D)  1.88 
A)  0.41 
B)  0.53 
C)  0.45 
D)  1.88

Question 20

The graph of an exponential function is given. Match the graph to one of the following functions.
-  A) $f ( x ) = 4 ^ { X } + 1$

Accepted Answer

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

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places. - $\log _ { 8 } 0.537$

Solve the problem. -The size P of a certain insect population at time t (in days) obeys the function $\mathrm { P } = 700 \mathrm { e } ^ { 0.03 \mathrm { t } }$ After how many days will the population reach 1500?

Express as a single logarithm. - $\log _ { \mathrm { c } } \mathrm { m } + \log _ { \mathrm { c } } \mathrm { n }$

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

Find the domain of the composite function f $f ^ { \circ } g$ - $f ( x ) = \frac { x } { x + 7 } ; \quad g ( x ) = \frac { 7 } { x + 5 }$

Solve the equation. - $\ln x + \ln ( x + 4 ) = 1$

Use the graph of the given one-to-one function to sketch the graph of the inverse function. For convenience, the graph of y = x is also given. - A) B) C) D)

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

Solve the problem. Round your answer to three decimals. -How long will it take for an investment to double in value if it earns 9.25% compounded continuously?

Solve the problem. -Tracey bought a diamond ring appraised at $1,700 at an antique store. If diamonds have appreciated in value at an annual rate of 10%, what was the value of the ring 10 years ago? (Round your answer to the nearest dollar.)

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

Approximate the value using a calculator. Express answer rounded to three decimal places. - $\mathrm { e } ^ { - 2.7 }$

Change the exponential expression to an equivalent expression involving a logarithm. - $13 ^ { x } = 169$

Graph the function. - $f(x)=-4 \ln x$ $Graph the function. - f(x)=-4 \ln x A) B) C) D)$ A) $Graph the function. - f(x)=-4 \ln x A) B) C) D)$ B) $Graph the function. - f(x)=-4 \ln x A) B) C) D)$ C) $Graph the function. - f(x)=-4 \ln x A) B) C) D)$ D) $Graph the function. - f(x)=-4 \ln x A) B) C) D)$

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - $\log _ { 6,9 } 2.8$

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

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places. - log⁡80.537\log _ { 8 } 0.537log8​0.537

Solve the problem. -The size P of a certain insect population at time t (in days) obeys the function P=700e0.03t\mathrm { P } = 700 \mathrm { e } ^ { 0.03 \mathrm { t } }P=700e0.03t After how many days will the population reach 1500?

Express as a single logarithm. - log⁡cm+log⁡cn\log _ { \mathrm { c } } \mathrm { m } + \log _ { \mathrm { c } } \mathrm { n }logc​m+logc​n

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

Find the domain of the composite function f f∘gf ^ { \circ } g f∘g - f(x)=xx+7;g(x)=7x+5f ( x ) = \frac { x } { x + 7 } ; \quad g ( x ) = \frac { 7 } { x + 5 }f(x)=x+7x​;g(x)=x+57​

Solve the equation. - ln⁡x+ln⁡(x+4)=1\ln x + \ln ( x + 4 ) = 1lnx+ln(x+4)=1

Graph the function. - f(x)=e−0.3xf ( x ) = e ^ { - 0.3 x }f(x)=e−0.3x A) B) C) D)

Use the graph of the given one-to-one function to sketch the graph of the inverse function. For convenience, the graph of y = x is also given. - A) B) C) D)

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)=5x+4f ( x ) = \sqrt { 5 x + 4 }f(x)=5x+4​

Solve the problem. Round your answer to three decimals. -How long will it take for an investment to double in value if it earns 9.25% compounded continuously?

Solve the problem. -Tracey bought a diamond ring appraised at $1,700 at an antique store. If diamonds have appreciated in value at an annual rate of 10%, what was the value of the ring 10 years ago? (Round your answer to the nearest dollar.)

Solve the exponential equation. Express the solution set in terms of natural logarithms. - e3x=6e ^ { 3 x } = 6e3x=6

Approximate the value using a calculator. Express answer rounded to three decimal places. - e−2.7\mathrm { e } ^ { - 2.7 }e−2.7

Change the exponential expression to an equivalent expression involving a logarithm. - 13x=16913 ^ { x } = 16913x=169

Graph the function. - f(x)=−4ln⁡xf(x)=-4 \ln xf(x)=−4lnx A) B) C) D)

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - log⁡6,92.8\log _ { 6,9 } 2.8log6,9​2.8

The graph of an exponential function is given. Match the graph to one of the following functions. - A) f(x)=4X+1f ( x ) = 4 ^ { X } + 1f(x)=4X+1 B) f(x)=4xf ( x ) = 4 ^ { x }f(x)=4x C) f(x)=4x−1f ( x ) = 4 ^ { x } - 1f(x)=4x−1 D) f(x)=4x+1f ( x ) = 4 ^ { x + 1 }f(x)=4x+1

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

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places. - $\log _ { 8 } 0.537$

Solve the problem. -The size P of a certain insect population at time t (in days) obeys the function $\mathrm { P } = 700 \mathrm { e } ^ { 0.03 \mathrm { t } }$ After how many days will the population reach 1500?

Express as a single logarithm. - $\log _ { \mathrm { c } } \mathrm { m } + \log _ { \mathrm { c } } \mathrm { n }$

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

Find the domain of the composite function f $f ^ { \circ } g$ - $f ( x ) = \frac { x } { x + 7 } ; \quad g ( x ) = \frac { 7 } { x + 5 }$

Solve the equation. - $\ln x + \ln ( x + 4 ) = 1$

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

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

Approximate the value using a calculator. Express answer rounded to three decimal places. - $\mathrm { e } ^ { - 2.7 }$

Change the exponential expression to an equivalent expression involving a logarithm. - $13 ^ { x } = 169$

Graph the function. - $f(x)=-4 \ln x$ $Graph the function. - f(x)=-4 \ln x A) B) C) D)$ A) $Graph the function. - f(x)=-4 \ln x A) B) C) D)$ B) $Graph the function. - f(x)=-4 \ln x A) B) C) D)$ C) $Graph the function. - f(x)=-4 \ln x A) B) C) D)$ D) $Graph the function. - f(x)=-4 \ln x A) B) C) D)$

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - $\log _ { 6,9 } 2.8$