Question 1

Write the word or phrase that best completes each statement or answers the question.
-$$4 \frac { 3 } { 4 } \% \text { compounded quarterly }$$

Accepted Answer

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

Question 2

Write the word or phrase that best completes each statement or answers the question.
-The price $p$ of a certain product and the quantity sold $x$ obey the demand equation $p = - \frac { 2 } { 3 } x + 200,0 \leq x \leq 300$.
Suppose that the cost $C$ of producing $x$ units is $C = \frac { \sqrt { x } } { 20 } + 800$. Assuming that all items produced are sold, find the cost $C$ as a function of the price $p$.

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 exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the
solution.
-$$\left( \frac { 1 } { 2 } \right) ^ { x } = 15$$

Accepted Answer

A)  $\{ - 0.26 \}$ 
B)  $\{ - 7.50 \}$ 
C)  $\{ 3.91 \}$ 
D)  $\{ - 3.91 \}$ 
A)  $\{ - 0.26 \}$ 
B)  $\{ - 7.50 \}$ 
C)  $\{ 3.91 \}$ 
D)  $\{ - 3.91 \}$

Question 4

Choose the one alternative that best completes the statement or answers the question.
-The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential
) When will the account be worth $1,856? $$\text { growth model } \mathrm { A } = 1,400 \mathrm { e } ^ { 0.047 \mathrm { t } }$$

Accepted Answer

A)  2006 
B)  2005 
C)  2007 
D)  2008 
A)  2006 
B)  2005 
C)  2007 
D)  2008

Question 5

Change the exponential expression to an equivalent expression involving a logarithm.
-$$x ^ { \sqrt { 5 } } = \pi$$

Accepted Answer

A)  $x = \log _ { \pi } \sqrt { 5 }$ 
B)  $x = \log _ { \sqrt { 5 } } \pi$ 
C)  $\sqrt { 5 } = \log _ { \pi } \mathrm { x }$ 
D)  $\sqrt { 5 } = \log _ { \mathrm { X } } \pi$ 
A)  $x = \log _ { \pi } \sqrt { 5 }$ 
B)  $x = \log _ { \sqrt { 5 } } \pi$ 
C)  $\sqrt { 5 } = \log _ { \pi } \mathrm { x }$ 
D)  $\sqrt { 5 } = \log _ { \mathrm { X } } \pi$

Question 6

Choose the one alternative that best completes the statement or answers the question.
Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the
solution.
-$$e ^ { x + 4 } = 7$$

Accepted Answer

A)  $\{ 2.56 \}$ 
B)  $\{ - 2.86 \}$ 
C)  $\{ - 2.44 \}$ 
D)  $\{ - 2.92 \}$ 
A)  $\{ 2.56 \}$ 
B)  $\{ - 2.86 \}$ 
C)  $\{ - 2.44 \}$ 
D)  $\{ - 2.92 \}$

Question 7

Find the value of the expression.
-Let $\log _ { b } A = 2$ and $\log _ { b } B = - 10$. Find $\log _ { b } \frac { A } { B }$.

Accepted Answer

A)  $- 8$ 
B)  12 
C)  $- \frac { 1 } { 5 }$ 
D)  $\frac { 1 } { 5 }$ 
A)  $- 8$ 
B)  12 
C)  $- \frac { 1 } { 5 }$ 
D)  $\frac { 1 } { 5 }$

Question 8

Solve the problem.
-Suppose that $\mathrm { f } ( \mathrm { x } ) = 5 ^ { \mathrm { x } } + 9$. What is $\mathrm { f } ( 5 )$ ? What point is on the graph of $\mathrm { f }$ ?

Accepted Answer

A)  3,$125 ; ( 9,3,125 )$ 
B)  3,134 ; $( 5,3,125 )$ 
C)  3,125 ; $( 5,3,125 )$ 
D)  3,$134 ; ( 5,3,134 )$ 
A)  3,$125 ; ( 9,3,125 )$ 
B)  3,134 ; $( 5,3,125 )$ 
C)  3,125 ; $( 5,3,125 )$ 
D)  3,$134 ; ( 5,3,134 )$

Question 9

Find the value of the expression.
-Let $\log _ { b } A = 5$ and $\log _ { b } B = - 4$. Find $\log _ { b } B ^ { 2 }$.

Accepted Answer

A)  $- 8$ 
B)  $- 16$ 
C)  16 
D)  10 
A)  $- 8$ 
B)  $- 16$ 
C)  16 
D)  10

Question 10

Solve the equation.
-$$2 + \log _ { 3 } ( 2 x + 5 ) - \log _ { 3 } x = 4$$

Accepted Answer

A)  $\left\{ \frac { 5 } { 4 } \right\}$ 
B)  $\left\{ \frac { 5 } { 7 } \right\}$ 
C)  $\left\{ \frac { 1 \pm \sqrt { 46 } } { 9 } \right\}$ 
D)  $\left\{ \frac { 1 + \sqrt { 46 } } { 9 } \right\}$ 
A)  $\left\{ \frac { 5 } { 4 } \right\}$ 
B)  $\left\{ \frac { 5 } { 7 } \right\}$ 
C)  $\left\{ \frac { 1 \pm \sqrt { 46 } } { 9 } \right\}$ 
D)  $\left\{ \frac { 1 + \sqrt { 46 } } { 9 } \right\}$

Question 11

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$8 \ln 3 x = 40$

Accepted Answer

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

Question 12

Solve the problem.
-The long jump record, in feet, at a particular school can be modeled by $\mathrm { f } ( \mathrm { x } ) = 19 + 2.5 \ln ( \mathrm { x } + 1 )$ where $\mathrm { x }$ is the number of years since records began to be kept at the school. What is the record for the long jump 25 years after record started being kept? Round your answer to the nearest tenth.

Accepted Answer

A)  $27.0$ feet 
B)  $26.9$ feet 
C)  $21.5$ feet 
D)  $27.1$ feet 
A)  $27.0$ feet 
B)  $26.9$ feet 
C)  $21.5$ feet 
D)  $27.1$ feet

Question 13

Solve the problem.
-The rabbit population in a forest area grows at the rate of 7% monthly. If there are 270 rabbits in September, find how many rabbits (rounded to the nearest whole number) should be expected by next September. Use $$y = 270 ( 2.7 ) ^ { 0.07 t }$$

Accepted Answer

A)  635 
B)  609 
C)  622 
D)  612 
A)  635 
B)  609 
C)  622 
D)  612

Question 14

Choose the one alternative that best completes the statement or answers the question.
-The half-life of plutonium-234 is 9 hours. If 60 milligrams is present now, how much will be present in 3 days? (Round your answer to three decimal places.)

Accepted Answer

A)  47.622 
B)  0.234 
C)  5.952 
D)  34.461 
A)  47.622 
B)  0.234 
C)  5.952 
D)  34.461

Question 15

Solve the equation.
-$$\mathrm { e } ^ { \mathrm { x } - 5 } = \left( \frac { 1 } { \mathrm { e } ^ { 5 } } \right) ^ { \mathrm { x } + 6 }$$

Accepted Answer

A)  $\left\{ - \frac { 35 } { 4 } \right\}$ 
B)  $\left\{ \frac { 11 } { 6 } \right\}$ 
C)  $\left\{ - \frac { 25 } { 6 } \right\}$ 
D)  $\left\{ - \frac { 11 } { 4 } \right\}$ 
A)  $\left\{ - \frac { 35 } { 4 } \right\}$ 
B)  $\left\{ \frac { 11 } { 6 } \right\}$ 
C)  $\left\{ - \frac { 25 } { 6 } \right\}$ 
D)  $\left\{ - \frac { 11 } { 4 } \right\}$

Question 16

Solve the problem.
-What principal invested at 8% compounded continuously for 4 years will yield $1190? Round the answer to two decimal places.

Accepted Answer

A)  $1638.78 
B)  $1188.62 
C)  $864.12 
D)  $627.48 
A)  $1638.78 
B)  $1188.62 
C)  $864.12 
D)  $627.48

Question 17

Write the word or phrase that best completes each statement or answers the question.
-Assume that the half-life of Carbon-14 is 5700 years. Find the age (to the nearest year) of a wooden axe in
which the amount of Carbon-14 is 30% of what it originally had.

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

Use a calculator to find the natural logarithm correct to four decimal places.
-$\ln \left( 1.65 \cdot e ^ { - 6 } \right)$

Accepted Answer

A)  $0.5008$ 
B)  $0.5023$ 
C)  $6.5008$ 
D)  $- 5.4992$ 
A)  $0.5008$ 
B)  $0.5023$ 
C)  $6.5008$ 
D)  $- 5.4992$

Question 20

Write as the sum and/or difference of logarithms. Express powers as factors.
-$\ln \sqrt [ 6 ] { \mathrm { ey } }$

Accepted Answer

A)  $6 \ln y + 6$ 
B)  $\frac { y } { 6 }$ 
C)  $\frac { 1 } { 6 } \ln \sqrt [ 6 ] { e _ { y } } + \frac { 1 } { 6 }$ 
D)  $\frac { 1 } { 6 } \ln y + \frac { 1 } { 6 }$ 
A)  $6 \ln y + 6$ 
B)  $\frac { y } { 6 }$ 
C)  $\frac { 1 } { 6 } \ln \sqrt [ 6 ] { e _ { y } } + \frac { 1 } { 6 }$ 
D)  $\frac { 1 } { 6 } \ln y + \frac { 1 } { 6 }$

Write the word or phrase that best completes each statement or answers the question. - $4 \frac { 3 } { 4 } \% \text { compounded quarterly }$

Choose the one alternative that best completes the statement or answers the question. Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $\left( \frac { 1 } { 2 } \right) ^ { x } = 15$

Change the exponential expression to an equivalent expression involving a logarithm. - $x ^ { \sqrt { 5 } } = \pi$

Choose the one alternative that best completes the statement or answers the question. Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $e ^ { x + 4 } = 7$

Find the value of the expression. -Let $\log _ { b } A = 2$ and $\log _ { b } B = - 10$ . Find $\log _ { b } \frac { A } { B }$ .

Solve the problem. -Suppose that $\mathrm { f } ( \mathrm { x } ) = 5 ^ { \mathrm { x } } + 9$ . What is $\mathrm { f } ( 5 )$ ? What point is on the graph of $\mathrm { f }$ ?

Find the value of the expression. -Let $\log _ { b } A = 5$ and $\log _ { b } B = - 4$ . Find $\log _ { b } B ^ { 2 }$ .

Solve the equation. - $2 + \log _ { 3 } ( 2 x + 5 ) - \log _ { 3 } x = 4$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $8 \ln 3 x = 40$

Solve the problem. -The rabbit population in a forest area grows at the rate of 7% monthly. If there are 270 rabbits in September, find how many rabbits (rounded to the nearest whole number) should be expected by next September. Use $y = 270 ( 2.7 ) ^ { 0.07 t }$

Choose the one alternative that best completes the statement or answers the question. -The half-life of plutonium-234 is 9 hours. If 60 milligrams is present now, how much will be present in 3 days? (Round your answer to three decimal places.)

Solve the equation. - $\mathrm { e } ^ { \mathrm { x } - 5 } = \left( \frac { 1 } { \mathrm { e } ^ { 5 } } \right) ^ { \mathrm { x } + 6 }$

Solve the problem. -What principal invested at 8% compounded continuously for 4 years will yield $1190? Round the answer to two decimal places.

Write the word or phrase that best completes each statement or answers the question. -Assume that the half-life of Carbon-14 is 5700 years. Find the age (to the nearest year) of a wooden axe in which the amount of Carbon-14 is 30% of what it originally had.

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

Use a calculator to find the natural logarithm correct to four decimal places. - $\ln \left( 1.65 \cdot e ^ { - 6 } \right)$

Write as the sum and/or difference of logarithms. Express powers as factors. - $\ln \sqrt [ 6 ] { \mathrm { ey } }$

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

Write the word or phrase that best completes each statement or answers the question. - 434% compounded quarterly 4 \frac { 3 } { 4 } \% \text { compounded quarterly }443​% compounded quarterly

Choose the one alternative that best completes the statement or answers the question. Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - (12)x=15\left( \frac { 1 } { 2 } \right) ^ { x } = 15(21​)x=15

Change the exponential expression to an equivalent expression involving a logarithm. - x5=πx ^ { \sqrt { 5 } } = \pix5​=π

Choose the one alternative that best completes the statement or answers the question. Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - ex+4=7e ^ { x + 4 } = 7ex+4=7

Find the value of the expression. -Let log⁡bA=2\log _ { b } A = 2logb​A=2 and log⁡bB=−10\log _ { b } B = - 10logb​B=−10 . Find log⁡bAB\log _ { b } \frac { A } { B }logb​BA​ .

Solve the problem. -Suppose that f(x)=5x+9\mathrm { f } ( \mathrm { x } ) = 5 ^ { \mathrm { x } } + 9f(x)=5x+9 . What is f(5)\mathrm { f } ( 5 )f(5) ? What point is on the graph of f\mathrm { f }f ?

Find the value of the expression. -Let log⁡bA=5\log _ { b } A = 5logb​A=5 and log⁡bB=−4\log _ { b } B = - 4logb​B=−4 . Find log⁡bB2\log _ { b } B ^ { 2 }logb​B2 .

Solve the equation. - 2+log⁡3(2x+5)−log⁡3x=42 + \log _ { 3 } ( 2 x + 5 ) - \log _ { 3 } x = 42+log3​(2x+5)−log3​x=4

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - 8ln⁡3x=408 \ln 3 x = 408ln3x=40

Solve the problem. -The rabbit population in a forest area grows at the rate of 7% monthly. If there are 270 rabbits in September, find how many rabbits (rounded to the nearest whole number) should be expected by next September. Use y=270(2.7)0.07ty = 270 ( 2.7 ) ^ { 0.07 t }y=270(2.7)0.07t

Choose the one alternative that best completes the statement or answers the question. -The half-life of plutonium-234 is 9 hours. If 60 milligrams is present now, how much will be present in 3 days? (Round your answer to three decimal places.)

Solve the equation. - ex−5=(1e5)x+6\mathrm { e } ^ { \mathrm { x } - 5 } = \left( \frac { 1 } { \mathrm { e } ^ { 5 } } \right) ^ { \mathrm { x } + 6 }ex−5=(e51​)x+6

Solve the problem. -What principal invested at 8% compounded continuously for 4 years will yield $1190? Round the answer to two decimal places.

Write the word or phrase that best completes each statement or answers the question. -Assume that the half-life of Carbon-14 is 5700 years. Find the age (to the nearest year) of a wooden axe in which the amount of Carbon-14 is 30% of what it originally had.

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

Use a calculator to find the natural logarithm correct to four decimal places. - ln⁡(1.65⋅e−6)\ln \left( 1.65 \cdot e ^ { - 6 } \right)ln(1.65⋅e−6)

Write as the sum and/or difference of logarithms. Express powers as factors. - ln⁡ey6\ln \sqrt [ 6 ] { \mathrm { ey } }ln6ey​

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

Write the word or phrase that best completes each statement or answers the question. - $4 \frac { 3 } { 4 } \% \text { compounded quarterly }$

Choose the one alternative that best completes the statement or answers the question. Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $\left( \frac { 1 } { 2 } \right) ^ { x } = 15$

Change the exponential expression to an equivalent expression involving a logarithm. - $x ^ { \sqrt { 5 } } = \pi$

Choose the one alternative that best completes the statement or answers the question. Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $e ^ { x + 4 } = 7$

Find the value of the expression. -Let $\log _ { b } A = 2$ and $\log _ { b } B = - 10$ . Find $\log _ { b } \frac { A } { B }$ .

Solve the problem. -Suppose that $\mathrm { f } ( \mathrm { x } ) = 5 ^ { \mathrm { x } } + 9$ . What is $\mathrm { f } ( 5 )$ ? What point is on the graph of $\mathrm { f }$ ?

Find the value of the expression. -Let $\log _ { b } A = 5$ and $\log _ { b } B = - 4$ . Find $\log _ { b } B ^ { 2 }$ .

Solve the equation. - $2 + \log _ { 3 } ( 2 x + 5 ) - \log _ { 3 } x = 4$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $8 \ln 3 x = 40$

Solve the problem. -The rabbit population in a forest area grows at the rate of 7% monthly. If there are 270 rabbits in September, find how many rabbits (rounded to the nearest whole number) should be expected by next September. Use $y = 270 ( 2.7 ) ^ { 0.07 t }$

Solve the equation. - $\mathrm { e } ^ { \mathrm { x } - 5 } = \left( \frac { 1 } { \mathrm { e } ^ { 5 } } \right) ^ { \mathrm { x } + 6 }$

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

Use a calculator to find the natural logarithm correct to four decimal places. - $\ln \left( 1.65 \cdot e ^ { - 6 } \right)$

Write as the sum and/or difference of logarithms. Express powers as factors. - $\ln \sqrt [ 6 ] { \mathrm { ey } }$