Question 1

Determine whether the statement is true or false.
-Any polynomial function of odd degree is a one-to-one function.

Accepted Answer

A) True 
 B)False

Question 2

Write the word or phrase that best completes each statement or answers the question.
-A sample of 200 grams of radioactive substance decays according to the function $A ( t ) = 200 \mathrm { e } ^ { - .048 t }$, where $t$ is the time in years. How much of the substance will be left in the sample after 20 years? Round your answer to the nearest whole gram.

Accepted Answer

A)  $0 \mathrm {~g}$ 
B)  $77 \mathrm {~g}$ 
C)  $423 \mathrm {~g}$ 
D)  $1 \mathrm {~g}$ 
A)  $0 \mathrm {~g}$ 
B)  $77 \mathrm {~g}$ 
C)  $423 \mathrm {~g}$ 
D)  $1 \mathrm {~g}$

Question 3

Provide an appropriate response.
-Give an equation of the form $f ( x ) = a ^ { x }$ to define the exponential function whose graph contains the point $( 3,216 )$. Assume that a $> 0$.

Accepted Answer

A)  $f ( x ) = 729^ x$ 
B)  $f ( x ) = 46,656 ^ { x }$ 
C)  $f ( x ) = 6 ^ { x }$ 
D)  $f ( x ) = 18 ^ { x }$ 
A)  $f ( x ) = 729^ x$ 
B)  $f ( x ) = 46,656 ^ { x }$ 
C)  $f ( x ) = 6 ^ { x }$ 
D)  $f ( x ) = 18 ^ { x }$

Question 4

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ
-$$f ( x ) = - 6 x + 1$$

Accepted Answer

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

Question 5

Solve the problem.
-If $\mathrm { f } ( \mathrm { x } ) = \ln \mathrm { x }$, find $\mathrm { f } \left( \mathrm { e } ^ { 10 \ln 3 } \right)$.

Accepted Answer

A)  $10 \ln 3$ 
B)  $\ln 3$ 
C)  $\mathrm { e } ^ { 3 }$ 
D)  $3 \ln 10$ 
A)  $10 \ln 3$ 
B)  $\ln 3$ 
C)  $\mathrm { e } ^ { 3 }$ 
D)  $3 \ln 10$

Question 6

Solve the problem. Round your answer to the nearest tenth, when appropriate. Use the formula $$\mathrm { pH } = - \log \left[ \mathrm { H } _ { 3 } \mathrm { O } ^ { + } \right]$$ as needed.
-Find $\left[ \mathrm { H } _ { 3 } \mathrm { O } ^ { + } \right]$if the $\mathrm { pH } = 1.4$.

Accepted Answer

A)  $4.0 \times 10 ^ { - 2 }$ 
B)  $2.5 \times 10 ^ { - 1 }$ 
C)  $4.0 \times 10 ^ { - 1 }$ 
D)  $2.5 \times 10 ^ { - 2 }$ 
A)  $4.0 \times 10 ^ { - 2 }$ 
B)  $2.5 \times 10 ^ { - 1 }$ 
C)  $4.0 \times 10 ^ { - 1 }$ 
D)  $2.5 \times 10 ^ { - 2 }$

Question 7

Given $$\log _ { 10 } 2 = 0.3010 \text { and } \log _ { 10 } 3 = 0.4771 \text {, }$$ find the logarithm without using a calculator.
-$\log _ { 10 } 6$

Accepted Answer

A)  $0.9542$ 
B)  $0.7781$ 
C)  $0.1436$ 
D)  $0.903$ 
A)  $0.9542$ 
B)  $0.7781$ 
C)  $0.1436$ 
D)  $0.903$

Question 8

Solve the problem.
-The height in meters of women of a certain tribe is approximated by $h = 0.52 + 2 \log ( t / 3 )$ where $t$ is the woman's age in years and $1 \leq t \leq 20$. Estimate the height (to the nearest hundredth) of a woman of the tribe 4 years of age.

Accepted Answer

A)  $0.96 \mathrm {~m}$ 
B)  $0.52 \mathrm {~m}$ 
C)  $1.12 \mathrm {~m}$ 
D)  $0.77 \mathrm {~m}$ 
A)  $0.96 \mathrm {~m}$ 
B)  $0.52 \mathrm {~m}$ 
C)  $1.12 \mathrm {~m}$ 
D)  $0.77 \mathrm {~m}$

Question 9

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ
-$$f ( x ) = \sqrt { x - 3 } , x \geq 3$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \sqrt { x + 3 }$ 
B)  $f ^ { - 1 } ( x ) = x ^ { 2 } + 3 , x \geq 0$ 
C)  not a one-to-one 
D)  $f ^ { - 1 } ( x ) = ( x - 3 ) ^ { 2 }$ 
A)  $f ^ { - 1 } ( x ) = \sqrt { x + 3 }$ 
B)  $f ^ { - 1 } ( x ) = x ^ { 2 } + 3 , x \geq 0$ 
C)  not a one-to-one 
D)  $f ^ { - 1 } ( x ) = ( x - 3 ) ^ { 2 }$

Question 10

Write the word or phrase that best completes each statement or answers the question.
-Assume the cost of a car is $\$ 23,000$. With continuous compounding in effect, find the number of years it would take to double the cost of the car at an annual inflation rate of $6.5 \%$. Round the answer to the nearest hundredth.

Accepted Answer

A)  $154.51 \mathrm { yr }$ 
B)  $10.66 \mathrm { yr }$ 
C)  $1.55 \mathrm { yr }$ 
D)  $165.18 \mathrm { yr }$ 
A)  $154.51 \mathrm { yr }$ 
B)  $10.66 \mathrm { yr }$ 
C)  $1.55 \mathrm { yr }$ 
D)  $165.18 \mathrm { yr }$

Question 11

Determine whether the statement is true or false.
-If a function f has an inverse function, then f is one-to-one.

Accepted Answer

A) True 
 B)False

Question 12

Decide whether the pair of functions graphed are inverses.
-

Accepted Answer

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

Question 13

Write the word or phrase that best completes each statement or answers the question.
-A certain radioactive isotope decays at a rate of $0.15 \%$ annually. Determine the half-life of this isotope, to the nearest year.

Accepted Answer

A)  $201 \mathrm { yr }$ 
B)  $333 \mathrm { yr }$ 
C)  $5 \mathrm { yr }$ 
D)  $462 \mathrm { yr }$ 
A)  $201 \mathrm { yr }$ 
B)  $333 \mathrm { yr }$ 
C)  $5 \mathrm { yr }$ 
D)  $462 \mathrm { yr }$

Question 14

Write the word or phrase that best completes each statement or answers the question.
-Coffee is best enjoyed at a temperature of $125 ^ { \circ } \mathrm { F }$. A restaurant owner wants to discover the temperature $\mathrm { T }$ at which he should serve his coffee so that it will have cooled to this ideal temperature in 3 minutes. He discovers that a cup of coffee served at $199 ^ { \circ } \mathrm { F }$ cools to $181 ^ { \circ } \mathrm { F }$ in one minute when his restaurant is at $69 ^ { \circ } \mathrm { F }$. If he maintains the restaurant temperature at $69 ^ { \circ } \mathrm { F }$, at what temperature should he serve the coffee to meet his goal?

Accepted Answer

A)  $157 ^ { \circ } \mathrm { F }$ 
B)  $177 ^ { \circ } \mathrm { F }$ 
C)  $199 ^ { \circ } \mathrm { F }$ 
D)  $152 ^ { \circ } \mathrm { F }$ 
A)  $157 ^ { \circ } \mathrm { F }$ 
B)  $177 ^ { \circ } \mathrm { F }$ 
C)  $199 ^ { \circ } \mathrm { F }$ 
D)  $152 ^ { \circ } \mathrm { F }$

Question 15

Write in logarithmic form.
-$10 ^ { - 5 } = 0.00001$

Accepted Answer

A)  $\log _ { 5 } - 5 = 0.10$ 
B)  $\log _ { 10 } 0.00001 = - 5$ 
C)  $\log _ { 10 } - 5 = 0.00001$ 
D)  $\log _ { 5 } 0.10 = - 5$ 
A)  $\log _ { 5 } - 5 = 0.10$ 
B)  $\log _ { 10 } 0.00001 = - 5$ 
C)  $\log _ { 10 } - 5 = 0.00001$ 
D)  $\log _ { 5 } 0.10 = - 5$

Question 16

Write an equivalent expression in exponential form.
-$\log _ { 10 } 100,000 = 5$

Accepted Answer

A)  $10100,000 = 5$ 
B)  $10 ^ { 5 } = 100,000$ 
C)  $100,000 ^ { 5 } = 10$ 
D)  $510 = 100,000$ 
A)  $10100,000 = 5$ 
B)  $10 ^ { 5 } = 100,000$ 
C)  $100,000 ^ { 5 } = 10$ 
D)  $510 = 100,000$

Question 17

Write the word or phrase that best completes each statement or answers the question.
-A population is increasing according to the exponential function defined by $\mathrm { y } = 3 \mathrm { e } \cdot 04 \mathrm { x }$, where $\mathrm { y }$ is in millions and $\mathrm { x }$ is the number of years. Which of the following should be done in order to answer the question "How long will it take for the population to quadruple?"

Accepted Answer

A)  Solve $3 \mathrm { e } \cdot 04 \mathrm { x } = 4$. 
B)  Evaluate $y = 3 \mathrm { e } \cdot 04 ( 4 )$. 
C)  Evaluate $y = 3 e ^ { - 04 ( 1 / 4 ) }$. 
D)  Solve $3 \mathrm { e } \cdot 04 \mathrm { x } = 12$. 
A)  Solve $3 \mathrm { e } \cdot 04 \mathrm { x } = 4$. 
B)  Evaluate $y = 3 \mathrm { e } \cdot 04 ( 4 )$. 
C)  Evaluate $y = 3 e ^ { - 04 ( 1 / 4 ) }$. 
D)  Solve $3 \mathrm { e } \cdot 04 \mathrm { x } = 12$.

Question 18

Graph the function.
-$f(x)=\left(\frac{5}{2}\right)^{x}$

Accepted Answer

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

Question 19

Decide whether or not the functions are inverses of each other.Use the definition of inverses to determine whether f and g are inverses.
-$$f ( x ) = 2 x + 4 , \quad g ( x ) = \frac { 1 } { 2 } x - 2$$

Accepted Answer

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

Question 20

Solve the equation.
-$( \sqrt { 5 } ) ^ { x + 3 } = 25 ^ { x }$

Accepted Answer

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

Determine whether the statement is true or false. -Any polynomial function of odd degree is a one-to-one function.

Provide an appropriate response. -Give an equation of the form $f ( x ) = a ^ { x }$ to define the exponential function whose graph contains the point $( 3,216 )$ . Assume that a $> 0$ .

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ - $f ( x ) = - 6 x + 1$

Solve the problem. -If $\mathrm { f } ( \mathrm { x } ) = \ln \mathrm { x }$ , find $\mathrm { f } \left( \mathrm { e } ^ { 10 \ln 3 } \right)$ .

Solve the problem. Round your answer to the nearest tenth, when appropriate. Use the formula $\mathrm { pH } = - \log \left[ \mathrm { H } _ { 3 } \mathrm { O } ^ { + } \right]$ as needed. -Find $\left[ \mathrm { H } _ { 3 } \mathrm { O } ^ { + } \right]$ if the $\mathrm { pH } = 1.4$ .

Given $\log _ { 10 } 2 = 0.3010 \text { and } \log _ { 10 } 3 = 0.4771 \text {, }$ find the logarithm without using a calculator. - $\log _ { 10 } 6$

Solve the problem. -The height in meters of women of a certain tribe is approximated by $h = 0.52 + 2 \log ( t / 3 )$ where $t$ is the woman's age in years and $1 \leq t \leq 20$ . Estimate the height (to the nearest hundredth) of a woman of the tribe 4 years of age.

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ - $f ( x ) = \sqrt { x - 3 } , x \geq 3$

Determine whether the statement is true or false. -If a function f has an inverse function, then f is one-to-one.

Decide whether the pair of functions graphed are inverses. -

Write the word or phrase that best completes each statement or answers the question. -A certain radioactive isotope decays at a rate of $0.15 \%$ annually. Determine the half-life of this isotope, to the nearest year.

Write in logarithmic form. - $10 ^ { - 5 } = 0.00001$

Write an equivalent expression in exponential form. - $\log _ { 10 } 100,000 = 5$

Graph the function. - $f(x)=\left(\frac{5}{2}\right)^{x}$ $Graph the function. - f(x)=\left(\frac{5}{2}\right)^{x}$

Decide whether or not the functions are inverses of each other.Use the definition of inverses to determine whether f and g are inverses. - $f ( x ) = 2 x + 4 , \quad g ( x ) = \frac { 1 } { 2 } x - 2$

Solve the equation. - $( \sqrt { 5 } ) ^ { x + 3 } = 25 ^ { x }$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

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Exam 4: Inverse, Exponential, and Logarithmic Functions