Question 1

Find the value. Give an approximation to four decimal places.
-$\ln 26,700,000$

Accepted Answer

A)  $7.4265$ 
B)  $5.5872$ 
C)  $0.0583$ 
D)  $17.1002$ 
A)  $7.4265$ 
B)  $5.5872$ 
C)  $0.0583$ 
D)  $17.1002$ D

Question 2

Round your answer to the nearest tenth, when appropriate. Use the formula $\mathrm { pH } = - \log \left[ \mathrm { H } _ { 3 } \mathrm { O } ^ { + } \right] , \text {as }$ needed.
-Find the $\mathrm { pH }$ if $\left[ \mathrm { H } _ { 3 } \mathrm { O } ^ { + } \right] = 6.6 \times 10 ^ { - 14 }$

Accepted Answer

A)  $14.2$ 
B)  $14.8$ 
C)  $13.2$ 
D)  $13.8$ 
A)  $14.2$ 
B)  $14.8$ 
C)  $13.2$ 
D)  $13.8$ C

Question 3

Find the value. Give an approximation to four decimal places.
-$\ln 131 - \ln 27$

Accepted Answer

A)  $- 5.0939$ 
B)  $8.1710$ 
C)  $1.5794$ 
D)  $1.4792$ 
A)  $- 5.0939$ 
B)  $8.1710$ 
C)  $1.5794$ 
D)  $1.4792$ C

Question 4

Solve the equation.
-$$\left( \frac { 1 } { 3 } \right) ^ { 6 x + 4 } = 9 ^ { x - 5 }$$

Accepted Answer

A)  $\left\{ \frac { 3 } { 4 } \right\}$ 
B)  $\left\{ \frac { 1 } { 7 } \right\}$ 
C)  $\left\{ \frac { 7 } { 3 } \right\}$ 
D)  $\left\{ \frac { 1 } { 8 } \right\}$ 
A)  $\left\{ \frac { 3 } { 4 } \right\}$ 
B)  $\left\{ \frac { 1 } { 7 } \right\}$ 
C)  $\left\{ \frac { 7 } { 3 } \right\}$ 
D)  $\left\{ \frac { 1 } { 8 } \right\}$

Question 5

Solve the following graphically. If necessary, round answers to the nearest thousandth.
-$$500 ( 1 - 0.03 ) ^ { 2 x } = 250$$

Accepted Answer

A)  $\{ - 46.900 \}$ 
B)  $\{ - 192.652 \}$ 
C)  $\{ 11.378 \}$ 
D)  $\{ 45.5131461 \}$ 
A)  $\{ - 46.900 \}$ 
B)  $\{ - 192.652 \}$ 
C)  $\{ 11.378 \}$ 
D)  $\{ 45.5131461 \}$

Question 6

Use a graphing calculator to graph the function using the given viewing window. Use the graph to decide if the function
is one-to-one. If the function is one-to-one, give the equation of the inverse function.
-$$f ( x ) = \frac { x + 1 } { x - 4 } ; [ - 10,10 ] \text { by } [ - 10,10 ]$$

Accepted Answer

A)  one-to-one; $f ^ { - 1 } ( x ) = \frac { 4 x - 1 } { x + 1 }$ 
B)  one-to-one; $f ^ { - 1 } ( x ) = \frac { x - 4 } { x + 1 }$ 
C)  one-to-one; $f ^ { - 1 } ( x ) = \frac { 4 x + 1 } { x - 1 }$ 
D)  not one-to-one 
A)  one-to-one; $f ^ { - 1 } ( x ) = \frac { 4 x - 1 } { x + 1 }$ 
B)  one-to-one; $f ^ { - 1 } ( x ) = \frac { x - 4 } { x + 1 }$ 
C)  one-to-one; $f ^ { - 1 } ( x ) = \frac { 4 x + 1 } { x - 1 }$ 
D)  not one-to-one

Question 7

Write an equivalent expression in exponential form.
-$$\log _ { 5 } \frac { 1 } { 125 } = x$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 25 } \right\}$ 
B)  $\{ 3 \}$ 
C)  $\{ - 3 \}$ 
D)  $\left\{ \frac { 1 } { 625 } \right\}$ 
A)  $\left\{ \frac { 1 } { 25 } \right\}$ 
B)  $\{ 3 \}$ 
C)  $\{ - 3 \}$ 
D)  $\left\{ \frac { 1 } { 625 } \right\}$

Question 8

Find the domain and range of the inverse of the given function.
-$$f ( x ) = 8 - x ^ { 2 } ; x \geq 0$$

Accepted Answer

A)  Domain: $( - \infty , 8 ]$; range: range: $[ 0 , \infty )$ 
B)  Domain: all real numbers; range: $[ - 8 , \infty )$ 
C)  Domain: all real numbers; range: $( - \infty , 8 ]$ 
D)  Domain and range: all real numbers 
A)  Domain: $( - \infty , 8 ]$; range: range: $[ 0 , \infty )$ 
B)  Domain: all real numbers; range: $[ - 8 , \infty )$ 
C)  Domain: all real numbers; range: $( - \infty , 8 ]$ 
D)  Domain and range: all real numbers

Question 9

Provide an appropriate response.
-Why can' $$y = 2 ^ { x }$$ have an x-intercept?

Accepted Answer

Because no

Question 10

Choose the one alternative that best completes the statement or answers the question.
-The population of a particular city is increasing at a rate proportional to its size. It follows the function $P ( t ) = 1 + k e ^ { 0.03 t }$ where k is a constant and t is the time in years. If the current population
Is 47,000, in how many years is the population expected to be 117,500?

Accepted Answer

A)  31 yr 
B)  193 yr 
C)  18 yr 
D)  13 yr 
A)  31 yr 
B)  193 yr 
C)  18 yr 
D)  13 yr

Question 11

Find the present value of the future value.
-$2000, invested for 5 years at 4% compounded quarterly

Accepted Answer

A)  $1659.09 
B)  $2420.38 
C)  $2440.38 
D)  $1639.09 
A)  $1659.09 
B)  $2420.38 
C)  $2440.38 
D)  $1639.09

Question 12

Write an equation for the graph given. The graph represents an exponential function f with base 2 or 3, translated and/or
reflected.
-

Accepted Answer

A)  $2 ^ { - x } - 1$ 
B)  $2 ^ { x } - 1$ 
C)  $- 2 ^ { x } - 1$ 
D)  $2 ^ { - x } + 1$ 
A)  $2 ^ { - x } - 1$ 
B)  $2 ^ { x } - 1$ 
C)  $- 2 ^ { x } - 1$ 
D)  $2 ^ { - x } + 1$

Question 13

Solve the problem.
-How long will it take for $1900 to grow to $2200 at an interest rate of 3.7% if the interest is compounded quarterly? Round the number of years to the nearest hundredth.

Accepted Answer

A)  3.98 yr 
B)  4.04 yr 
C)  15.92 yr 
D)  31.44 yr 
A)  3.98 yr 
B)  4.04 yr 
C)  15.92 yr 
D)  31.44 yr

Question 14

Write an equivalent expression in exponential form.
-$$\log _ { 625 } 5 = \frac { 1 } { 4 }$$

Accepted Answer

A)  $\left( \frac { 1 } { 4 } \right) ^ { 5 } = 625$ 
B)  $625 ^ { 1 / 4 } = 5$ 
C)  $5625 = 4$ 
D)  $5 ^ { 1 / 4 } = 625$ 
A)  $\left( \frac { 1 } { 4 } \right) ^ { 5 } = 625$ 
B)  $625 ^ { 1 / 4 } = 5$ 
C)  $5625 = 4$ 
D)  $5 ^ { 1 / 4 } = 625$

Question 15

Find the present value of the future value.
-Find the required annual interest rate, to the nearest tenth of a percent, for $5200 to grow to $6500 if interest is compounded quarterly for 7 years.

Accepted Answer

A)  1.6% 
B)  0.8% 
C)  4.0% 
D)  3.2% 
A)  1.6% 
B)  0.8% 
C)  4.0% 
D)  3.2%

Question 16

rite the word or phrase that best completes each statement or answers the question.
-$$\text { Between what two integers does the solution of } 5 x = 73 \text { lie? Explain your answer. }$$

Accepted Answer

The soluti

Question 17

The graph of a function f is given. Use the graph to find the indicated value.
-$\mathrm{f}^{-1}(2)$

Accepted Answer

A)  $\frac { 2 } { 3 }$ 
B)  6 
C)  2 
D)  $\frac { 3 } { 2 }$ 
A)  $\frac { 2 } { 3 }$ 
B)  6 
C)  2 
D)  $\frac { 3 } { 2 }$

Question 18

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

Accepted Answer

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

Question 19

Write in logarithmic form.
-$10 ^ { 4 } = 10,000$

Accepted Answer

A)  $\log _ { 4 } 10,000 = 10$ 
B)  $\log _ { 10 } 10,000 = 4$ 
C)  $\log _ { 10 } 4 = 10,000$ 
D)  $\log _ { 4 } 10 = 10,000$ 
A)  $\log _ { 4 } 10,000 = 10$ 
B)  $\log _ { 10 } 10,000 = 4$ 
C)  $\log _ { 10 } 4 = 10,000$ 
D)  $\log _ { 4 } 10 = 10,000$

Question 20

Write the word or phrase that best completes each statement or answers the question.
-Given $f ( x ) = \log _ { 5 } x$, evaluate the following.
(a) $f \left( 5 ^ { 3 } \right)$
(b) $f \left( 5 \log _ { 5 } 5 \right)$
(c) f(55 $\left. \log _ { 5 } 5 \right)$

Accepted Answer

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

Find the value. Give an approximation to four decimal places. - $\ln 26,700,000$

Round your answer to the nearest tenth, when appropriate. Use the formula $\mathrm { pH } = - \log \left[ \mathrm { H } _ { 3 } \mathrm { O } ^ { + } \right] , \text {as }$ needed. -Find the $\mathrm { pH }$ if $\left[ \mathrm { H } _ { 3 } \mathrm { O } ^ { + } \right] = 6.6 \times 10 ^ { - 14 }$

Find the value. Give an approximation to four decimal places. - $\ln 131 - \ln 27$

Solve the equation. - $\left( \frac { 1 } { 3 } \right) ^ { 6 x + 4 } = 9 ^ { x - 5 }$

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $500 ( 1 - 0.03 ) ^ { 2 x } = 250$

Use a graphing calculator to graph the function using the given viewing window. Use the graph to decide if the function is one-to-one. If the function is one-to-one, give the equation of the inverse function. - $f ( x ) = \frac { x + 1 } { x - 4 } ; [ - 10,10 ] \text { by } [ - 10,10 ]$

Write an equivalent expression in exponential form. - $\log _ { 5 } \frac { 1 } { 125 } = x$

Find the domain and range of the inverse of the given function. - $f ( x ) = 8 - x ^ { 2 } ; x \geq 0$

Provide an appropriate response. -Why can' $y = 2 ^ { x }$ have an x-intercept?

Find the present value of the future value. -$2000, invested for 5 years at 4% compounded quarterly

Write an equation for the graph given. The graph represents an exponential function f with base 2 or 3, translated and/or reflected. -

Solve the problem. -How long will it take for $1900 to grow to $2200 at an interest rate of 3.7% if the interest is compounded quarterly? Round the number of years to the nearest hundredth.

Write an equivalent expression in exponential form. - $\log _ { 625 } 5 = \frac { 1 } { 4 }$

Find the present value of the future value. -Find the required annual interest rate, to the nearest tenth of a percent, for $5200 to grow to $6500 if interest is compounded quarterly for 7 years.

rite the word or phrase that best completes each statement or answers the question. - $\text { Between what two integers does the solution of } 5 x = 73 \text { lie? Explain your answer. }$

The graph of a function f is given. Use the graph to find the indicated value. - $\mathrm{f}^{-1}(2)$ $The graph of a function f is given. Use the graph to find the indicated value. - \mathrm{f}^{-1}(2)$

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

Write in logarithmic form. - $10 ^ { 4 } = 10,000$

Write the word or phrase that best completes each statement or answers the question. -Given $f ( x ) = \log _ { 5 } x$ , evaluate the following. (a) $f \left( 5 ^ { 3 } \right)$ (b) $f \left( 5 \log _ { 5 } 5 \right)$ (c) f(55 $\left. \log _ { 5 } 5 \right)$

Review of Basic Concepts

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

Filters

Exam 5: Inverse, Exponential, and Logarithmic Functions

Find the value. Give an approximation to four decimal places. - ln⁡26,700,000\ln 26,700,000ln26,700,000

Find the value. Give an approximation to four decimal places. - ln⁡131−ln⁡27\ln 131 - \ln 27ln131−ln27

Solve the equation. - (13)6x+4=9x−5\left( \frac { 1 } { 3 } \right) ^ { 6 x + 4 } = 9 ^ { x - 5 }(31​)6x+4=9x−5

Solve the following graphically. If necessary, round answers to the nearest thousandth. - 500(1−0.03)2x=250500 ( 1 - 0.03 ) ^ { 2 x } = 250500(1−0.03)2x=250

Write an equivalent expression in exponential form. - log⁡51125=x\log _ { 5 } \frac { 1 } { 125 } = xlog5​1251​=x

Find the domain and range of the inverse of the given function. - f(x)=8−x2;x≥0f ( x ) = 8 - x ^ { 2 } ; x \geq 0f(x)=8−x2;x≥0

Provide an appropriate response. -Why can' y=2xy = 2 ^ { x }y=2x have an x-intercept?