Question 1

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator.
-$\ln e ^ { \sqrt { 7 } }$

Accepted Answer

A)  7 
B)  49 
C)  e 
D)  $\sqrt { 7 }$ 
A)  7 
B)  49 
C)  e 
D)  $\sqrt { 7 }$

Question 2

Solve the equation.
-$\log _ { y } 14 = 2$

Accepted Answer

A)  $\left\{ 14 ^ { 2 } \right\}$ 
B)  $\left\{ \frac { 14 } { 2 } \right\}$ 
C)  $\left\{ 2 ^ { 1 / 14 } \right\}$ 
D)  $\left\{ 14 ^ { 1 / 2 } \right\}$ 
A)  $\left\{ 14 ^ { 2 } \right\}$ 
B)  $\left\{ \frac { 14 } { 2 } \right\}$ 
C)  $\left\{ 2 ^ { 1 / 14 } \right\}$ 
D)  $\left\{ 14 ^ { 1 / 2 } \right\}$

Question 3

Change the logarithmic expression to an equivalent expression involving an exponent.
-$$\log _ { 3 } \frac { 1 } { 27 } = - 3$$

Accepted Answer

A)  $\left( \frac { 1 } { 27 } \right) ^ { 3 } = 3$ 
B)  $3 ^ { 27 } = 3$ 
C)  $3 ^ { 3 } = \frac { 1 } { 27 }$ 
D)  $3 ^ { - 3 } = \frac { 1 } { 27 }$ 
A)  $\left( \frac { 1 } { 27 } \right) ^ { 3 } = 3$ 
B)  $3 ^ { 27 } = 3$ 
C)  $3 ^ { 3 } = \frac { 1 } { 27 }$ 
D)  $3 ^ { - 3 } = \frac { 1 } { 27 }$

Question 4

The function f is one-to-one. Find its inverse.
-$$f ( x ) = x ^ { 2 } + 1 , x \geq 0$$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } } - 1 , \mathrm { x } \geq 0$ 
B)  $f ^ { - 1 } ( x ) = \sqrt { x - 1 } , x \geq 1$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } + 1 } , \mathrm { x } \geq - 1$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } } - 1 , \mathrm { x } < 0$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } } - 1 , \mathrm { x } \geq 0$ 
B)  $f ^ { - 1 } ( x ) = \sqrt { x - 1 } , x \geq 1$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } + 1 } , \mathrm { x } \geq - 1$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } } - 1 , \mathrm { x } < 0$

Question 5

Write the word or phrase that best completes each statement or answers the question.
-The temperature (in degrees Fahrenheit) of a dead body that has been cooling in a room set at $70 ^ { \circ }$ is measured as $88 ^ { \circ }$. One hour later, the body temperature is $87.5 ^ { \circ }$. How long (to the nearest hour) before the first measurement was the time of death, assuming that the body temperature of the deceased at the time of death was $98.6 ^ { \circ }$. Assume the cooling follows Newton's Law of Cooling:
$$\mathrm { U } = \mathrm { T } + \left( \mathrm { U } _ { \mathrm { O } } - \mathrm { T } \right) \mathrm { e } ^ { \mathrm { kt } }$$

Accepted Answer

The deceased died ap

Question 6

Solve the problem.
-The number of men dying of AIDS (in thousands) since 1987 is modeled by $y = 17.3 + 10.06 ( \ln x )$, where $x$ represents the number of years after 1987. Use this model to predict the number of AIDS deaths among men in 1994. Express answer rounded to the nearest hundred men.

Accepted Answer

A)  36,900 
B)  26,000 
C)  37,000 
D)  25,800 
A)  36,900 
B)  26,000 
C)  37,000 
D)  25,800

Question 7

Solve the equation.
-$$4 ( 1 + 2 x ) = 1,024$$

Accepted Answer

A)  $\{ 8 \}$ 
B)  $\{ 2 \}$ 
C)  $\{ - 2 \}$ 
D)  $\{ 256 \}$ 
A)  $\{ 8 \}$ 
B)  $\{ 2 \}$ 
C)  $\{ - 2 \}$ 
D)  $\{ 256 \}$

Question 8

Write the word or phrase that best completes each statement or answers the question.
-What is the magnitude of an earthquake whose seismographic reading is 0.94 millimeters at a distance of 100
kilometers from its epicenter?

Accepted Answer

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

Question 9

Decide whether or not the functions are inverses of each other.
-$$f ( x ) = x ^ { 3 } - 8 , g ( x ) = \sqrt [ 3 ] { x + 8 }$$

Accepted Answer

A)  $\mathrm { No }$ 
B)  Yes 
A)  $\mathrm { No }$ 
B)  Yes

Question 10

Choose the one alternative that best completes the statement or answers the question.
Find the effective rate of interest.
-12% compounded continuously

Accepted Answer

A)  12.75% 
B)  12.089% 
C)  12.451% 
D)  12.374% 
A)  12.75% 
B)  12.089% 
C)  12.451% 
D)  12.374%

Question 11

Choose the one alternative that best completes the statement or answers the question.
-The half-life of silicon-32 is 710 years. If 10 grams is present now, how much will be present in 800 years? (Round your answer to three decimal places.)

Accepted Answer

A)  0.004 
B)  9.249 
C)  4.579 
D)  0 
A)  0.004 
B)  9.249 
C)  4.579 
D)  0

Question 12

Solve the equation.
-$$3 ^{( 9 - 4 x )} = 3$$

Accepted Answer

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

Question 13

Write the word or phrase that best completes each statement or answers the question.
-The revenue for a dot.com company is projected to double each year for the first 5 years. If the revenue for the
first year is $2 million, write a function showing the revenue R after x years. What is the revenue for the fourth
year?

Accepted Answer

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

Question 14

Choose the one alternative that best completes the statement or answers the question.
-In $y = 8$

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 15

Write the word or phrase that best completes each statement or answers the question.
-$$\frac { e ^ { X } - e ^ { - x } } { 2 } = - 1$$

Accepted Answer

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

Question 16

Use the horizontal line test to determine whether the function is one-to-one.
-

Accepted Answer

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

Question 17

Solve the exponential equation. Express the solution set in terms of natural logarithms.
-$$6 ^ { 8 x } = 2.2$$

Accepted Answer

A)  $\left\{ \frac { 2.2 \ln 8 } { \ln 6 } \right\}$ 
B)  $\left\{ \frac { \ln 2.2 } { 6 \ln 8 } \right\}$ 
C)  $\left\{ \frac { 8 \ln 2.2 } { \ln 6 } \right\}$ 
D)  $\left\{ \frac { \ln 2.2 } { 8 \ln 6 } \right\}$ 
A)  $\left\{ \frac { 2.2 \ln 8 } { \ln 6 } \right\}$ 
B)  $\left\{ \frac { \ln 2.2 } { 6 \ln 8 } \right\}$ 
C)  $\left\{ \frac { 8 \ln 2.2 } { \ln 6 } \right\}$ 
D)  $\left\{ \frac { \ln 2.2 } { 8 \ln 6 } \right\}$

Question 18

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)  $f ( x ) = \log _ { 2 } ( x - 2 )$ 
B)  $f ( x ) = \log _ { 2 } ( x + 2 )$ 
C)  $f ( x ) = \log _ { 2 } x - 2$ 
D)  $f ( x ) = \log _ { 2 } x$ 
A)  $f ( x ) = \log _ { 2 } ( x - 2 )$ 
B)  $f ( x ) = \log _ { 2 } ( x + 2 )$ 
C)  $f ( x ) = \log _ { 2 } x - 2$ 
D)  $f ( x ) = \log _ { 2 } x$

Question 19

Write the word or phrase that best completes each statement or answers the question.
-The concentration of alcohol in a person's blood is measurable. Suppose that the risk R (given as a percent) of having an
accident while driving a car can be modeled by the equation $$\mathrm { R } = 4 \mathrm { e } ^ { \mathrm { kx } }$$ where x is the variable concentration of alcohol in the blood and k is a constant.
(a) Suppose that a concentration of alcohol in the blood of 0.09 results in a 14% risk (R = 14) of an accident. Find the
constant k in the equation.
(b) Using this value of k, what is the risk if the concentration is 0.014?
(c) Using the same value of k, what concentration of alcohol corresponds to a risk of 100%?
(d) If the law asserts that anyone with a risk of having an accident of 12 or more should not have driving privileges,
at what concentration of alcohol in the blood should a driver be arrested and charged with a DUI?

Accepted Answer

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

Question 20

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.
-$$f ( x ) = \frac { 4 } { 6 x + 5 }$$

Accepted Answer

A)  $f ( x ) : D = \left\{ x \mid x \neq \frac { 2 } { 3 } \right\} , R = \left\{ y \mid y \neq \frac { 4 } { 5 } \right\}$
$$f ^ { - 1 } ( x ) : D = \left\{ x \mid x \neq \frac { 4 } { 5 } \right\} , R = \left\{ y \mid y \neq \frac { 2 } { 3 } \right\}$$ 
B)  $f ( x ) : D = \left\{ x \mid x \neq \frac { 5 } { 6 } \right\} , R = \{ y | y z - 5 \rangle$;
$$f ^ { - 1 } ( x ) : D = \{ x \mid x \neq - 5 \} , R = \left\{ y \mid y \neq \frac { 5 } { 6 } \right\}$$ 
C)  $f ( x )$ : D is all real numbers, $R$ is all real numbers;
$\mathrm { f } ^ { - 1 } ( \mathrm { x } )$ : D is all real numbers, $\mathrm { R }$ is all real numbers 
D)  $f ( x ) : D = \left\{ x \mid x \neq - \frac { 5 } { 6 } \right\} , R = \{ y \mid y \neq 0 \}$;
$$f ^ { - 1 } ( x ) : D = \{ x \mid x \neq 0 \} , R = \left\{ y \mid y z - \frac { 5 } { 6 } \right\}$$ 
A)  $f ( x ) : D = \left\{ x \mid x \neq \frac { 2 } { 3 } \right\} , R = \left\{ y \mid y \neq \frac { 4 } { 5 } \right\}$
$$f ^ { - 1 } ( x ) : D = \left\{ x \mid x \neq \frac { 4 } { 5 } \right\} , R = \left\{ y \mid y \neq \frac { 2 } { 3 } \right\}$$ 
B)  $f ( x ) : D = \left\{ x \mid x \neq \frac { 5 } { 6 } \right\} , R = \{ y | y z - 5 \rangle$;
$$f ^ { - 1 } ( x ) : D = \{ x \mid x \neq - 5 \} , R = \left\{ y \mid y \neq \frac { 5 } { 6 } \right\}$$ 
C)  $f ( x )$ : D is all real numbers, $R$ is all real numbers;
$\mathrm { f } ^ { - 1 } ( \mathrm { x } )$ : D is all real numbers, $\mathrm { R }$ is all real numbers 
D)  $f ( x ) : D = \left\{ x \mid x \neq - \frac { 5 } { 6 } \right\} , R = \{ y \mid y \neq 0 \}$;
$$f ^ { - 1 } ( x ) : D = \{ x \mid x \neq 0 \} , R = \left\{ y \mid y z - \frac { 5 } { 6 } \right\}$$

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - $\ln e ^ { \sqrt { 7 } }$

Solve the equation. - $\log _ { y } 14 = 2$

Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { 3 } \frac { 1 } { 27 } = - 3$

The function f is one-to-one. Find its inverse. - $f ( x ) = x ^ { 2 } + 1 , x \geq 0$

Solve the problem. -The number of men dying of AIDS (in thousands) since 1987 is modeled by $y = 17.3 + 10.06 ( \ln x )$ , where $x$ represents the number of years after 1987. Use this model to predict the number of AIDS deaths among men in 1994. Express answer rounded to the nearest hundred men.

Solve the equation. - $4 ( 1 + 2 x ) = 1,024$

Write the word or phrase that best completes each statement or answers the question. -What is the magnitude of an earthquake whose seismographic reading is 0.94 millimeters at a distance of 100 kilometers from its epicenter?

Decide whether or not the functions are inverses of each other. - $f ( x ) = x ^ { 3 } - 8 , g ( x ) = \sqrt [ 3 ] { x + 8 }$

Choose the one alternative that best completes the statement or answers the question. Find the effective rate of interest. -12% compounded continuously

Choose the one alternative that best completes the statement or answers the question. -The half-life of silicon-32 is 710 years. If 10 grams is present now, how much will be present in 800 years? (Round your answer to three decimal places.)

Solve the equation. - $3 ^{( 9 - 4 x )} = 3$

Choose the one alternative that best completes the statement or answers the question. -In $y = 8$

Write the word or phrase that best completes each statement or answers the question. - $\frac { e ^ { X } - e ^ { - x } } { 2 } = - 1$

Use the horizontal line test to determine whether the function is one-to-one. -

Solve the exponential equation. Express the solution set in terms of natural logarithms. - $6 ^ { 8 x } = 2.2$

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. -

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. - $f ( x ) = \frac { 4 } { 6 x + 5 }$

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

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - ln⁡e7\ln e ^ { \sqrt { 7 } }lne7​

Solve the equation. - log⁡y14=2\log _ { y } 14 = 2logy​14=2

Change the logarithmic expression to an equivalent expression involving an exponent. - log⁡3127=−3\log _ { 3 } \frac { 1 } { 27 } = - 3log3​271​=−3

The function f is one-to-one. Find its inverse. - f(x)=x2+1,x≥0f ( x ) = x ^ { 2 } + 1 , x \geq 0f(x)=x2+1,x≥0

Solve the equation. - 4(1+2x)=1,0244 ( 1 + 2 x ) = 1,0244(1+2x)=1,024

Write the word or phrase that best completes each statement or answers the question. -What is the magnitude of an earthquake whose seismographic reading is 0.94 millimeters at a distance of 100 kilometers from its epicenter?

Decide whether or not the functions are inverses of each other. - f(x)=x3−8,g(x)=x+83f ( x ) = x ^ { 3 } - 8 , g ( x ) = \sqrt [ 3 ] { x + 8 }f(x)=x3−8,g(x)=3x+8​

Choose the one alternative that best completes the statement or answers the question. Find the effective rate of interest. -12% compounded continuously

Choose the one alternative that best completes the statement or answers the question. -The half-life of silicon-32 is 710 years. If 10 grams is present now, how much will be present in 800 years? (Round your answer to three decimal places.)

Solve the equation. - 3(9−4x)=33 ^{( 9 - 4 x )} = 33(9−4x)=3

Choose the one alternative that best completes the statement or answers the question. -In y=8y = 8y=8

Write the word or phrase that best completes each statement or answers the question. - eX−e−x2=−1\frac { e ^ { X } - e ^ { - x } } { 2 } = - 12eX−e−x​=−1

Use the horizontal line test to determine whether the function is one-to-one. -

Solve the exponential equation. Express the solution set in terms of natural logarithms. - 68x=2.26 ^ { 8 x } = 2.268x=2.2

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. -

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)=46x+5f ( x ) = \frac { 4 } { 6 x + 5 }f(x)=6x+54​

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

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - $\ln e ^ { \sqrt { 7 } }$

Solve the equation. - $\log _ { y } 14 = 2$

Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { 3 } \frac { 1 } { 27 } = - 3$

The function f is one-to-one. Find its inverse. - $f ( x ) = x ^ { 2 } + 1 , x \geq 0$

Solve the equation. - $4 ( 1 + 2 x ) = 1,024$

Decide whether or not the functions are inverses of each other. - $f ( x ) = x ^ { 3 } - 8 , g ( x ) = \sqrt [ 3 ] { x + 8 }$

Solve the equation. - $3 ^{( 9 - 4 x )} = 3$

Choose the one alternative that best completes the statement or answers the question. -In $y = 8$

Write the word or phrase that best completes each statement or answers the question. - $\frac { e ^ { X } - e ^ { - x } } { 2 } = - 1$

Solve the exponential equation. Express the solution set in terms of natural logarithms. - $6 ^ { 8 x } = 2.2$

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. - $f ( x ) = \frac { 4 } { 6 x + 5 }$