Question 1

Solve for the indicated variable.
-$I = \frac { n } { R } \left( 1 - e ^ { - a w / 3 } \right)$, for $w$

Accepted Answer

A)  $w = \frac { 3 \cdot \ln ( 1 - a ) } { \operatorname { In } R }$ 
B)  $w = - \frac { 3 \ln ( 1 - \operatorname { IRn } ) } { a }$ 
C)  $w = - \frac { 3 } { a } \ln \left( 1 - \frac { \mathrm { IR } } { \mathrm { n } } \right)$ 
D)  $w = \frac { \operatorname { In } R \cdot \ln ( 1 - a ) } { 3 }$ 
A)  $w = \frac { 3 \cdot \ln ( 1 - a ) } { \operatorname { In } R }$ 
B)  $w = - \frac { 3 \ln ( 1 - \operatorname { IRn } ) } { a }$ 
C)  $w = - \frac { 3 } { a } \ln \left( 1 - \frac { \mathrm { IR } } { \mathrm { n } } \right)$ 
D)  $w = \frac { \operatorname { In } R \cdot \ln ( 1 - a ) } { 3 }$

Question 2

Write the word or phrase that best completes each statement or answers the question.
-The population growth of an animal species is described by $F ( t ) = 400 \log ( 2 t + 3 )$ where $t$ is measured in months. Find the population of this species in an area 6 months after the species is introduced.

Accepted Answer

A)  704 
B)  240 
C)  470 
D)  74 
A)  704 
B)  240 
C)  470 
D)  74

Question 3

Determine the function value.
-Suppose f(x) = loga(x) and f(7) = 2. Find f(343).

Accepted Answer

A)  3 
B)  7 
C)  6 
D)  12 
A)  3 
B)  7 
C)  6 
D)  12

Question 4

Decide whether the pair of functions graphed are inverses.
-

Accepted Answer

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

Question 5

Solve the following graphically. If necessary, round answers to the nearest thousandth.
-$\log x ^ { 2 } = ( \log x ) ^ { 2 }$

Accepted Answer

A)  $\{ 1,10.000 \}$ 
B)  $\{ 1,100 \}$ 
C)  $\{ 1,2 \}$ 
D)  $\{ 0,1 \}$ 
A)  $\{ 1,10.000 \}$ 
B)  $\{ 1,100 \}$ 
C)  $\{ 1,2 \}$ 
D)  $\{ 0,1 \}$

Question 6

Find the function value. If the result is irrational, round your answer to the nearest thousandth.
-Let f(x) = 5x. Find f(3).

Accepted Answer

A)  3125 
B)  125 
C)  15 
D)  243 
A)  3125 
B)  125 
C)  15 
D)  243

Question 7

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 the $\mathrm { pH }$ if $\left[ \mathrm { H } _ { 3 } \mathrm { O } ^ { + } \right] = 3.9 \times 10 ^ { - 8 }$.

Accepted Answer

A)  $7.6$ 
B)  $7.4$ 
C)  $8.4$ 
D)  $8.6$ 
A)  $7.6$ 
B)  $7.4$ 
C)  $8.4$ 
D)  $8.6$

Question 8

Solve the equation and express the solution in exact form.
-$\log _ { 7 } x ^ { 2 } = ( \log 7 x ) ^ { 2 }$

Accepted Answer

A)  $\{ 49 \}$ 
B)  $\{ 0,7 \}$ 
C)  $\{ 1,49 \}$ 
D)  $\{ 1,7 \}$ 
A)  $\{ 49 \}$ 
B)  $\{ 0,7 \}$ 
C)  $\{ 1,49 \}$ 
D)  $\{ 1,7 \}$

Question 9

Evaluate the logarithm.
-$\log _ { 18 } 1$

Accepted Answer

A)  1 
B)  18 
C)  0 
D)  10 
A)  1 
B)  18 
C)  0 
D)  10

Question 10

Find the value. Give an approximation to four decimal places.
-$\log 243$

Accepted Answer

A)  $2.3856$ 
B)  $2.3838$ 
C)  $5.4931$ 
D)  $2.3874$ 
A)  $2.3856$ 
B)  $2.3838$ 
C)  $5.4931$ 
D)  $2.3874$

Question 11

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth.
-32x = 4x + 1

Accepted Answer

A)  {1.26} 
B)  {-4.82} 
C)  {2.26} 
D)  {1.71} 
A)  {1.26} 
B)  {-4.82} 
C)  {2.26} 
D)  {1.71}

Question 12

Decide whether the given functions are inverses.
-

Accepted Answer

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

Question 13

Graph the exponential function using transformations where appropriate.
-$f(x)=\left(\frac{1}{3}\right)^{x}+1$

Accepted Answer

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

Question 14

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers.
-$6 \log _ { a } t - \log _ { a } s$

Accepted Answer

A)  $\log _ { a } t ^ { 6 } \div \log _ { a } s$ 
B)  $\log _ { a } \left( t ^ { 6 } - s \right)$ 
C)  $\log _ { a } \left( \frac { t ^ { 6 } } { s } \right)$ 
D)  $\log _ { a } \left( \frac { 6 t } { s } \right)$ 
A)  $\log _ { a } t ^ { 6 } \div \log _ { a } s$ 
B)  $\log _ { a } \left( t ^ { 6 } - s \right)$ 
C)  $\log _ { a } \left( \frac { t ^ { 6 } } { s } \right)$ 
D)  $\log _ { a } \left( \frac { 6 t } { s } \right)$

Question 15

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ
-$$\{ ( - 2,4 ) , ( 2 , - 4 ) , ( 8 , - 2 ) , ( - 8,2 ) \}$$

Accepted Answer

A)  $\{ ( 4 , - 2 ) , ( - 4,2 ) , ( - 2,8 ) , ( 2 , - 8 ) \}$ 
B)  $\{ ( 4 , - 2 ) , ( - 4,2 ) , ( 8 , - 2 ) , ( 2 , - 8 ) \}$ 
C)  $\{ ( 4 , - 2 ) , ( - 4,2 ) , ( - 2 , - 8 ) , ( 2,8 ) \}$ 
D)  not one-to-one 
A)  $\{ ( 4 , - 2 ) , ( - 4,2 ) , ( - 2,8 ) , ( 2 , - 8 ) \}$ 
B)  $\{ ( 4 , - 2 ) , ( - 4,2 ) , ( 8 , - 2 ) , ( 2 , - 8 ) \}$ 
C)  $\{ ( 4 , - 2 ) , ( - 4,2 ) , ( - 2 , - 8 ) , ( 2,8 ) \}$ 
D)  not one-to-one

Question 16

Solve the equation.
-$$32 ^x - 4 = 8^{4 x}$$

Accepted Answer

A)  $\left\{ - \frac { 4 } { 3 } \right\}$ 
B)  $\left\{ - \frac { 4 } { 7 } \right\}$ 
C)  $\left\{ - \frac { 20 } { 7 } \right\}$ 
D)  $\{ - 10 \}$ 
A)  $\left\{ - \frac { 4 } { 3 } \right\}$ 
B)  $\left\{ - \frac { 4 } { 7 } \right\}$ 
C)  $\left\{ - \frac { 20 } { 7 } \right\}$ 
D)  $\{ - 10 \}$

Question 17

Write the word or phrase that best completes each statement or answers the question.
-The amount of particulate matter left in solution during a filtering process is given by the equation P = 400(2)-0.8n, where n is the number of filtering steps. Find the amounts left for n = 0 and n = 5.
(Round to the nearest whole number.)

Accepted Answer

A)  400, 13 
B)  800, 25 
C)  400, 6400 
D)  400, 25 
A)  400, 13 
B)  800, 25 
C)  400, 6400 
D)  400, 25

Question 18

Write the word or phrase that best completes each statement or answers the question.
-$$\text { Between what two integers does the solution of } 7 x = 83 \text { lie? Explain your answer. }$$

Accepted Answer

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

Question 19

Graph the exponential function using transformations where appropriate.
-$f(x)=3^{x}-5$

Accepted Answer

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

Question 20

Find the function value. If the result is irrational, round your answer to the nearest thousandth.
-Let $f ( x ) = 4 x$. Find $f \left( \frac { 5 } { 2 } \right)$.

Accepted Answer

A)  10 
B)  32 
C)  512 
D)  $1.741$ 
A)  10 
B)  32 
C)  512 
D)  $1.741$

Solve for the indicated variable. - $I = \frac { n } { R } \left( 1 - e ^ { - a w / 3 } \right)$ , for $w$

Write the word or phrase that best completes each statement or answers the question. -The population growth of an animal species is described by $F ( t ) = 400 \log ( 2 t + 3 )$ where $t$ is measured in months. Find the population of this species in an area 6 months after the species is introduced.

Determine the function value. -Suppose f(x) = loga(x) and f(7) = 2. Find f(343).

Decide whether the pair of functions graphed are inverses. -

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $\log x ^ { 2 } = ( \log x ) ^ { 2 }$

Find the function value. If the result is irrational, round your answer to the nearest thousandth. -Let f(x) = 5x. Find f(3).

Solve the equation and express the solution in exact form. - $\log _ { 7 } x ^ { 2 } = ( \log 7 x ) ^ { 2 }$

Evaluate the logarithm. - $\log _ { 18 } 1$

Find the value. Give an approximation to four decimal places. - $\log 243$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. -32x = 4x + 1

Decide whether the given functions are inverses. -

Graph the exponential function using transformations where appropriate. - $f(x)=\left(\frac{1}{3}\right)^{x}+1$ $Graph the exponential function using transformations where appropriate. - f(x)=\left(\frac{1}{3}\right)^{x}+1$

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers. - $6 \log _ { a } t - \log _ { a } s$

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ - $\{ ( - 2,4 ) , ( 2 , - 4 ) , ( 8 , - 2 ) , ( - 8,2 ) \}$

Solve the equation. - $32 ^x - 4 = 8^{4 x}$

Write the word or phrase that best completes each statement or answers the question. - $\text { Between what two integers does the solution of } 7 x = 83 \text { lie? Explain your answer. }$

Graph the exponential function using transformations where appropriate. - $f(x)=3^{x}-5$ $Graph the exponential function using transformations where appropriate. - f(x)=3^{x}-5$

Find the function value. If the result is irrational, round your answer to the nearest thousandth. -Let $f ( x ) = 4 x$ . Find $f \left( \frac { 5 } { 2 } \right)$ .

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

Filters

Exam 4: Inverse, Exponential, and Logarithmic Functions

Solve for the indicated variable. - I=nR(1−e−aw/3)I = \frac { n } { R } \left( 1 - e ^ { - a w / 3 } \right)I=Rn​(1−e−aw/3) , for www