Question 1

Match the function with its graph.
-$$f ( x ) = \log _ { 5 } ( x - 1 )$$

Accepted Answer

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

Question 2

Determine whether or not the function is one-to-one.
-

Accepted Answer

A) True 
 B)False

Question 3

Find the value. Give an approximation to four decimal places.
-$\log 629 - \log 328$

Accepted Answer

A)  1.1124 
B)  0.6511 
C)  0.2828 
D)  12.2371 
A)  1.1124 
B)  0.6511 
C)  0.2828 
D)  12.2371

Question 4

Find the function value. If the result is irrational, round your answer to the nearest thousandth.
-Let $f ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }$. Find $f \left( \frac { 5 } { 2 } \right)$

Accepted Answer

A)  $\frac { 5 } { 6 }$ 
B)  $0.064$ 
C)  $15.588$ 
D)  $1.357$ 
A)  $\frac { 5 } { 6 }$ 
B)  $0.064$ 
C)  $15.588$ 
D)  $1.357$

Question 5

Find the value. Give an approximation to four decimal places.
-log(320 × 39)

Accepted Answer

A)  21.1326 
B)  4.0962 
C)  9.4319 
D)  3.9859 
A)  21.1326 
B)  4.0962 
C)  9.4319 
D)  3.9859

Question 6

Let f(x) compute the cost of a rental car after x days of use at $45 per day. What is the interpretation of the solution of $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 96$ ?

Accepted Answer

A)  The cost of rental for 96 days 
B)  The cost of rental for 45 days 
C)  The number of days rented for $96 
D)  The number of days rented for $45 
A)  The cost of rental for 96 days 
B)  The cost of rental for 45 days 
C)  The number of days rented for $96 
D)  The number of days rented for $45

Question 7

$$\text { Explain why } \log _ { 2 } 13 \text { is between } 3 \text { and } 4 \text {. }$$

Accepted Answer

@#LAT-DLM& and @#LAT-DLM&. Since @#LAT-DLM&, then

Question 8

Use the alphabet coding method $$( A = 1 , B = 2 , C = 3 , \ldots Z = 26 )$$ to solve the problem.
-The function defined by $f ( x ) = 3 x - 4$ was used to encode a message as:
$\begin{array} { l l l l l l l l l l } 38 & 11 & 62 & 11 & 50 & - 1 & 17 & - 1 & 23 & 38 \end{array}$ Find the inverse function and determine the message.

Accepted Answer

The answer of Use the alphabet coding method \[( A...

Question 9

How long will it take a sample of radioactive substance to decay to half of its original amount, if it decays according to the functi $\mathrm { A } ( \mathrm { t } ) = 250 \mathrm { e } ^ { - .223 \mathrm { t } }$ , where t is the time in years? Round your answer to the nearest
Hundredth year.

Accepted Answer

A)  27.87 yr 
B)  55.75 yr 
C)  3.11 yr 
D)  24.76 yr 
A)  27.87 yr 
B)  55.75 yr 
C)  3.11 yr 
D)  24.76 yr

Question 10

Solve the equation.
-$$16 = b ^ { 2 / 5 }$$

Accepted Answer

A)  $\{ - 1024,1024 \}$ 
B)  $\{ 1024 \}$ 
C)  $\{ 4 \}$ 
D)  $\{ - 4,4 \}$ 
A)  $\{ - 1024,1024 \}$ 
B)  $\{ 1024 \}$ 
C)  $\{ 4 \}$ 
D)  $\{ - 4,4 \}$

Question 11

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth.
-$2 - x = 5 ^ { - x }$

Accepted Answer

A)  $\{ 3.26 \}$ 
B)  $\{ - 0.59,1.96 \}$ 
C)  $\{ 2.26 \}$ 
D)  $\{ 1.66 \}$ 
A)  $\{ 3.26 \}$ 
B)  $\{ - 0.59,1.96 \}$ 
C)  $\{ 2.26 \}$ 
D)  $\{ 1.66 \}$

Question 12

The sales of a mature product (one which has passed its peak) will decline according to the function $\mathrm { S } ( \mathrm { t } ) = \mathrm { S } _ { 0 } \mathrm { e } ^ { - \mathrm { at } }$, where $\mathrm { t }$ is time in years since the peak sales. Find the sales of a product 17 years after its peak sales if $\mathrm { a } = 0.24$ and $\mathrm { S } _ { 0 } = 50,900$.

Accepted Answer

A)  3,827,101 units 
B)  431 units 
C)  64,707 units 
D)  861 units 
A)  3,827,101 units 
B)  431 units 
C)  64,707 units 
D)  861 units

Question 13

Provide an appropriate response.
-Give an equation of the form $\mathrm { f } ( \mathrm { x } ) = \mathrm { a } ^ { \mathrm { x } }$ to define the exponential function whose graph contains the point ( 2,9 $)$. Assume that $a > 0$.

Accepted Answer

A)  $f ( x ) = 3 ^ { x }$ 
B)  $f ( x ) = 27 ^ { x }$ 
C)  $f ( x ) = 6 ^ { x }$ 
D)  $f ( x ) = 8 ^ { x }$ 
A)  $f ( x ) = 3 ^ { x }$ 
B)  $f ( x ) = 27 ^ { x }$ 
C)  $f ( x ) = 6 ^ { x }$ 
D)  $f ( x ) = 8 ^ { x }$

Question 14

Write an equivalent expression in exponential form.
-$$\log _ { 25 } 5 = \frac { 1 } { 2 }$$

Accepted Answer

A)  $51 / 2 = 25$ 
B)  $\left( \frac { 1 } { 2 } \right) ^ { 5 } = 25$ 
C)  $25 ^ { 1 / 2 } = 5$ 
D)  $525 = 2$ 
A)  $51 / 2 = 25$ 
B)  $\left( \frac { 1 } { 2 } \right) ^ { 5 } = 25$ 
C)  $25 ^ { 1 / 2 } = 5$ 
D)  $525 = 2$

Question 15

If $\mathrm { f } ( \mathrm { x } ) = \log _ { 3 } x$, find $\mathrm { f } \left( 3 ^ { 2 } \right)$.

Accepted Answer

A)  $\log _ { 2 } x$ 
B)  3 
C)  6 
D)  2 
A)  $\log _ { 2 } x$ 
B)  3 
C)  6 
D)  2

Question 16

The half-life of an element is $4.5 \times 10 ^ { 11 } \text { yr. }$
How long does it take a sample of the element to decay to $\frac { 2 } { 3 }$ of its original mass? Use $\mathrm { A } = \mathrm { A } _ { 0 } ( 0.5 ) ^ { ( \mathrm { t } / \mathrm { T } ) }$ where $\mathrm { A } 0$ is the initial amount,  T  is the half-life, and  t  is the time. (Express results in scientific notation, rounded to the nearest hundredth.)

Accepted Answer

A)  $2.63 \times 10 ^ { 11 } \mathrm { yr }$ 
B)  $5.83 \times 10 ^ { 11 } \mathrm { yr }$ 
C)  $1.29 \times 10 ^ { 11 } \mathrm { yr }$ 
D)  $1.26 \times 10 ^ { 11 } \mathrm { yr }$ 
A)  $2.63 \times 10 ^ { 11 } \mathrm { yr }$ 
B)  $5.83 \times 10 ^ { 11 } \mathrm { yr }$ 
C)  $1.29 \times 10 ^ { 11 } \mathrm { yr }$ 
D)  $1.26 \times 10 ^ { 11 } \mathrm { yr }$

Question 17

Determine whether or not the function is one-to-one.
-$f ( x ) = \sqrt { 16 - x ^ { 2 } }$

Accepted Answer

A) True 
 B)False

Question 18

Decide whether the pair of functions graphed are inverses.
-

Accepted Answer

A) True 
 B)False

Question 19

What is the domain of the function $y = \log _ { 8 } x ?$

Accepted Answer

A)  $( -\infty , \infty )$ 
B)  $( 0 , \infty )$ 
C)  $( 8 , \infty )$ 
D)  $[ 0 , \infty )$ 
A)  $( -\infty , \infty )$ 
B)  $( 0 , \infty )$ 
C)  $( 8 , \infty )$ 
D)  $[ 0 , \infty )$

Question 20

An earthquake had an intensity $10 ^ { 6.1 }$ times more powerful than a reference level earthquake, or $106.1 \cdot \mathrm { I } _ { 0 }$. What was the magnitude of this earthquake on the Richter scale? $\mathrm { R } = \log _ { 0 } \left( \mathrm { I } / \mathrm { I } _ { 0 } \right)$.

Accepted Answer

A)  $3.9$ 
B)  $16.1$ 
C)  14 
D)  $6.1$ 
A)  $3.9$ 
B)  $16.1$ 
C)  14 
D)  $6.1$

Match the function with its graph. - $f ( x ) = \log _ { 5 } ( x - 1 )$

Determine whether or not the function is one-to-one. -

Find the value. Give an approximation to four decimal places. - $\log 629 - \log 328$

Find the function value. If the result is irrational, round your answer to the nearest thousandth. -Let $f ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }$ . Find $f \left( \frac { 5 } { 2 } \right)$

Find the value. Give an approximation to four decimal places. -log(320 × 39)

Let f(x) compute the cost of a rental car after x days of use at $45 per day. What is the interpretation of the solution of $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 96$ ?

$\text { Explain why } \log _ { 2 } 13 \text { is between } 3 \text { and } 4 \text {. }$

Use the alphabet coding method $( A = 1 , B = 2 , C = 3 , \ldots Z = 26 )$ to solve the problem. -The function defined by $f ( x ) = 3 x - 4$ was used to encode a message as: 38 11 62 11 50 -1 17 -1 23 38 Find the inverse function and determine the message.

How long will it take a sample of radioactive substance to decay to half of its original amount, if it decays according to the functi $\mathrm { A } ( \mathrm { t } ) = 250 \mathrm { e } ^ { - .223 \mathrm { t } }$ , where t is the time in years? Round your answer to the nearest Hundredth year.

Solve the equation. - $16 = b ^ { 2 / 5 }$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $2 - x = 5 ^ { - x }$

Provide an appropriate response. -Give an equation of the form $\mathrm { f } ( \mathrm { x } ) = \mathrm { a } ^ { \mathrm { x } }$ to define the exponential function whose graph contains the point ( 2,9 $)$ . Assume that $a > 0$ .

Write an equivalent expression in exponential form. - $\log _ { 25 } 5 = \frac { 1 } { 2 }$

If $\mathrm { f } ( \mathrm { x } ) = \log _ { 3 } x$ , find $\mathrm { f } \left( 3 ^ { 2 } \right)$ .

Determine whether or not the function is one-to-one. - $f ( x ) = \sqrt { 16 - x ^ { 2 } }$

Decide whether the pair of functions graphed are inverses. -

What is the domain of the function $y = \log _ { 8 } x ?$

An earthquake had an intensity $10 ^ { 6.1 }$ times more powerful than a reference level earthquake, or $106.1 \cdot \mathrm { I } _ { 0 }$ . What was the magnitude of this earthquake on the Richter scale? $\mathrm { R } = \log _ { 0 } \left( \mathrm { I } / \mathrm { I } _ { 0 } \right)$ .

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 5: Inverse, Exponential, and Logarithmic Functions

Match the function with its graph. - f(x)=log⁡5(x−1)f ( x ) = \log _ { 5 } ( x - 1 )f(x)=log5​(x−1)

Determine whether or not the function is one-to-one. -

Find the value. Give an approximation to four decimal places. - log⁡629−log⁡328\log 629 - \log 328log629−log328

Find the function value. If the result is irrational, round your answer to the nearest thousandth. -Let f(x)=(13)xf ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }f(x)=(31​)x . Find f(52)f \left( \frac { 5 } { 2 } \right)f(25​)

Find the value. Give an approximation to four decimal places. -log(320 × 39)

Let f(x) compute the cost of a rental car after x days of use at $45 per day. What is the interpretation of the solution of f−1(x)=96\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 96f−1(x)=96 ?

Explain why log⁡213 is between 3 and 4. \text { Explain why } \log _ { 2 } 13 \text { is between } 3 \text { and } 4 \text {. } Explain why log2​13 is between 3 and 4.

Solve the equation. - 16=b2/516 = b ^ { 2 / 5 }16=b2/5

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - 2−x=5−x2 - x = 5 ^ { - x }2−x=5−x

Provide an appropriate response. -Give an equation of the form f(x)=ax\mathrm { f } ( \mathrm { x } ) = \mathrm { a } ^ { \mathrm { x } }f(x)=ax to define the exponential function whose graph contains the point ( 2,9 ))) . Assume that a>0a > 0a>0 .

Write an equivalent expression in exponential form. - log⁡255=12\log _ { 25 } 5 = \frac { 1 } { 2 }log25​5=21​

If f(x)=log⁡3x\mathrm { f } ( \mathrm { x } ) = \log _ { 3 } xf(x)=log3​x , find f(32)\mathrm { f } \left( 3 ^ { 2 } \right)f(32) .

Determine whether or not the function is one-to-one. - f(x)=16−x2f ( x ) = \sqrt { 16 - x ^ { 2 } }f(x)=16−x2​

Decide whether the pair of functions graphed are inverses. -

What is the domain of the function y=log⁡8x?y = \log _ { 8 } x ?y=log8​x?

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Match the function with its graph. - $f ( x ) = \log _ { 5 } ( x - 1 )$

Find the value. Give an approximation to four decimal places. - $\log 629 - \log 328$

Find the function value. If the result is irrational, round your answer to the nearest thousandth. -Let $f ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }$ . Find $f \left( \frac { 5 } { 2 } \right)$

Let f(x) compute the cost of a rental car after x days of use at $45 per day. What is the interpretation of the solution of $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 96$ ?

$\text { Explain why } \log _ { 2 } 13 \text { is between } 3 \text { and } 4 \text {. }$

Solve the equation. - $16 = b ^ { 2 / 5 }$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $2 - x = 5 ^ { - x }$

Provide an appropriate response. -Give an equation of the form $\mathrm { f } ( \mathrm { x } ) = \mathrm { a } ^ { \mathrm { x } }$ to define the exponential function whose graph contains the point ( 2,9 $)$ . Assume that $a > 0$ .

Write an equivalent expression in exponential form. - $\log _ { 25 } 5 = \frac { 1 } { 2 }$

If $\mathrm { f } ( \mathrm { x } ) = \log _ { 3 } x$ , find $\mathrm { f } \left( 3 ^ { 2 } \right)$ .

Determine whether or not the function is one-to-one. - $f ( x ) = \sqrt { 16 - x ^ { 2 } }$

What is the domain of the function $y = \log _ { 8 } x ?$