Question 1

Use Natural Logarithms
Evaluate or simplify the expression without using a calculator.
-$\ln \frac { 1 } { e ^ { 4 } }$

Accepted Answer

A)  $- 4$ 
B)  4 
C)  $\frac { 1 } { 4 }$ 
D)  $- \frac { 1 } { 4 }$ 
A)  $- 4$ 
B)  4 
C)  $\frac { 1 } { 4 }$ 
D)  $- \frac { 1 } { 4 }$

Question 2

Evaluate the expression without using a calculator.
-$8 ^ { \log _ { 8 } 18 }$

Accepted Answer

A)  18 
B)  8 
C)  26 
D)  $\log _ { 8 } 18$ 
A)  18 
B)  8 
C)  26 
D)  $\log _ { 8 } 18$

Question 3

Solve the problem.
-A city is growing at the rate of 0.3% annually. If there were 2,520,000 residents in the city in 1993, find how many (to the nearest ten-thousand)are living in that city in 2000. Use y = 2,520,000(2.7)0.003t.

Accepted Answer

A) 2,570,000 
B) 140,000 
C) 6,800,000 
D) 2,600,000 
A) 2,570,000 
B) 140,000 
C) 6,800,000 
D) 2,600,000

Question 4

Solve the problem.
-The function $f ( x ) = 300 ( 0.5 ) ^ { x / 100 }$ models the amount in pounds of a particular radioactive material stored in a concrete vault, where $x$ is the number of years since the material was put into the vault. Find the amount of radioactive material in the vault after 120 years. Round to the nearest whole number.

Accepted Answer

A)  131 pounds 
B)  168 pounds 
C)  180 pounds 
D)  125 pounds 
A)  131 pounds 
B)  168 pounds 
C)  180 pounds 
D)  125 pounds

Question 5

Solve the problem.
-Cindy will require $18,000 in 2 years to return to college to get an MBA degree. How much money should she ask her parents for now so that, if she invests it at 11% compounded continuously, she will have
Enough for school? (Round your answer to the nearest dollar.)

Accepted Answer

A) $14,445 
B) $14,609 
C) $22,429 
D) $11,593 
A) $14,445 
B) $14,609 
C) $22,429 
D) $11,593

Question 6

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm
whose coefficient is 1. Where possible, evaluate logarithmic expressions.
-$2 \log _ { y } 4 + \log _ { y } 3$

Accepted Answer

A)  $\log _ { \mathrm { y } } 48$ 
B)  $\log _ { \mathrm { y } } 24$ 
C)  $2 \log _ { \mathrm { y } } 12$ 
D)  $\log _ { y } 6$ 
A)  $\log _ { \mathrm { y } } 48$ 
B)  $\log _ { \mathrm { y } } 24$ 
C)  $2 \log _ { \mathrm { y } } 12$ 
D)  $\log _ { y } 6$

Question 7

Write the equation in its equivalent exponential form.
-$\log _ { 2 } 8 = 3$

Accepted Answer

A)  $2 ^ { 3 } = 8$ 
B)  $3 ^ { 2 } = 8$ 
C)  $28 = 3$ 
D)  $8 ^ { 3 } = 2$ 
A)  $2 ^ { 3 } = 8$ 
B)  $3 ^ { 2 } = 8$ 
C)  $28 = 3$ 
D)  $8 ^ { 3 } = 2$

Question 8

Use Natural Logarithms
Evaluate or simplify the expression without using a calculator.
-$\ln \mathrm { e } ^ { 20 \mathrm { x } }$

Accepted Answer

A)  $20 x$ 
B)  $- 20 x$ 
C)  $\mathrm { e } ^ { 20 \mathrm { x } }$ 
D)  $\frac { 1 } { 20 x }$ 
A)  $20 x$ 
B)  $- 20 x$ 
C)  $\mathrm { e } ^ { 20 \mathrm { x } }$ 
D)  $\frac { 1 } { 20 x }$

Question 9

Use the Product Rule
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 10 } ( 10 x )$

Accepted Answer

A)  $1 + \log _ { 10 } x$ 
B)  10 
C)  $x$ 
D)  1 
A)  $1 + \log _ { 10 } x$ 
B)  10 
C)  $x$ 
D)  1

Question 10

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm
whose coefficient is 1. Where possible, evaluate logarithmic expressions.
-$$\ln x + 3 \ln y$$

Accepted Answer

A)  $\ln x y ^ { 3 }$ 
B)  $\ln \frac { x } { v ^ { 3 } }$ 
C)  $\ln 3 x y$ 
D)  $\ln ( x + 3 y )$ 
A)  $\ln x y ^ { 3 }$ 
B)  $\ln \frac { x } { v ^ { 3 } }$ 
C)  $\ln 3 x y$ 
D)  $\ln ( x + 3 y )$

Question 11

Use the Definition of a Logarithm to Solve Logarithmic Equations
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic
expressions. Give the exact answer.
-$\log _ { 2 } x = 5$

Accepted Answer

A)  $\{ 32 \}$ 
B)  $\{ 10 \}$ 
C)  $\{ 25 \}$ 
D)  $\{ 2.32 \}$ 
A)  $\{ 32 \}$ 
B)  $\{ 10 \}$ 
C)  $\{ 25 \}$ 
D)  $\{ 2.32 \}$

Question 12

Graph the function by making a table of coordinates.
-$f(x)=\left(\frac{1}{3}\right)^{x}$

Accepted Answer

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

Question 13

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places,
for the solution.
-$$10 ^ { \mathrm { x } } = 2.92$$

Accepted Answer

A)  $0.47$ 
B)  $831.76$ 
C)  $1.07$ 
D)  $29.2$ 
A)  $0.47$ 
B)  $831.76$ 
C)  $1.07$ 
D)  $29.2$

Question 14

Model Exponential Growth and Decay
Solve.
-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 growth model $\mathrm { A } = 5600 \mathrm { e } ^ { 0.055 \mathrm { t } }$. How much did you initially invest in the account?

Accepted Answer

A)  $\$ 5600.00$ 
B)  $\$ 5916.63$ 
C)  $\$ 308.00$ 
D)  $\$ 2800.00$ 
A)  $\$ 5600.00$ 
B)  $\$ 5916.63$ 
C)  $\$ 308.00$ 
D)  $\$ 2800.00$

Question 15

Evaluate or simplify the expression without using a calculator.
-$7 \left( 10 ^ { \log 5.6 } \right)$

Accepted Answer

A)  $39.2$ 
B)  392 
C)  $3.92$ 
D)  $12.0594$ 
A)  $39.2$ 
B)  392 
C)  $3.92$ 
D)  $12.0594$

Question 16

Use Compound Interest Formulas
Use the compound interest formulas A $$A = P \left( 1 + \frac { r } { n } \right) \text { and } A = P e ^ { r t } \text { to solve }$$
-Find the accumulated value of an investment of $2000 at 10% compounded semiannually for 7 years.

Accepted Answer

A) $3959.86 
B) $3897.43 
C) $2814.20 
D) $3400.00 
A) $3959.86 
B) $3897.43 
C) $2814.20 
D) $3400.00

Question 17

Model Exponential Growth and Decay
Solve.
-The half-life of silicon-32 is 710 years. If 30 grams is present now, how much will be present in 300 years? (Round your answer to three decimal places.)

Accepted Answer

A) 22.383 
B) 29.134 
C) 1.604 
D) 0 
A) 22.383 
B) 29.134 
C) 1.604 
D) 0

Question 18

Use the One-to-One Property of Logarithms to Solve Logarithmic Equations
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic
expressions. Give the exact answer.
-$\log x + \log ( x - 1 ) = \log 6$

Accepted Answer

A)  $\{ 3 \}$ 
B)  $\{ - 2 \}$ 
C)  $\{ 3 , - 2 \}$ 
D)  $\left\{ \frac { 7 } { 2 } \right\}$ 
A)  $\{ 3 \}$ 
B)  $\{ - 2 \}$ 
C)  $\{ 3 , - 2 \}$ 
D)  $\left\{ \frac { 7 } { 2 } \right\}$

Question 19

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm
whose coefficient is 1. Where possible, evaluate logarithmic expressions.
-$$\frac { 1 } { 2 } \left( \log _ { 5 } ( r - 9 ) - \log _ { 5 } r \right)$$

Accepted Answer

A)  $\log _ { 5 } \sqrt { \frac { r - 9 } { r } }$ 
B)  $\log _ { 5 } \sqrt { \frac { \mathrm { r } - 9 } { 2 \mathrm { r } } }$ 
C)  $\log _ { 5 } \frac { \sqrt { r - 9 } } { r }$ 
D)  $\log _ { 5 } \frac { \mathrm { r } - 9 } { \sqrt { \mathrm { r } } }$ 
A)  $\log _ { 5 } \sqrt { \frac { r - 9 } { r } }$ 
B)  $\log _ { 5 } \sqrt { \frac { \mathrm { r } - 9 } { 2 \mathrm { r } } }$ 
C)  $\log _ { 5 } \frac { \sqrt { r - 9 } } { r }$ 
D)  $\log _ { 5 } \frac { \mathrm { r } - 9 } { \sqrt { \mathrm { r } } }$

Question 20

The graph of an exponential function is given. Select the function for the graph from the functions listed.
-

Accepted Answer

A)  $f ( x ) = 2 ^ { x }$ 
B)  $f ( x ) = 2 ^ { x - 2 }$ 
C)  $f ( x ) = 2 ^ { x } - 2$ 
D)  $f ( x ) = 2 ^ { x } + 2$ 
A)  $f ( x ) = 2 ^ { x }$ 
B)  $f ( x ) = 2 ^ { x - 2 }$ 
C)  $f ( x ) = 2 ^ { x } - 2$ 
D)  $f ( x ) = 2 ^ { x } + 2$

Use Natural Logarithms Evaluate or simplify the expression without using a calculator. - $\ln \frac { 1 } { e ^ { 4 } }$

Evaluate the expression without using a calculator. - $8 ^ { \log _ { 8 } 18 }$

Solve the problem. -A city is growing at the rate of 0.3% annually. If there were 2,520,000 residents in the city in 1993, find how many (to the nearest ten-thousand)are living in that city in 2000. Use y = 2,520,000(2.7)0.003t.

Solve the problem. -Cindy will require $18,000 in 2 years to return to college to get an MBA degree. How much money should she ask her parents for now so that, if she invests it at 11% compounded continuously, she will have Enough for school? (Round your answer to the nearest dollar.)

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $2 \log _ { y } 4 + \log _ { y } 3$

Write the equation in its equivalent exponential form. - $\log _ { 2 } 8 = 3$

Use Natural Logarithms Evaluate or simplify the expression without using a calculator. - $\ln \mathrm { e } ^ { 20 \mathrm { x } }$

Use the Product Rule Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 10 } ( 10 x )$

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $\ln x + 3 \ln y$

Use the Definition of a Logarithm to Solve Logarithmic Equations Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - $\log _ { 2 } x = 5$

Graph the function by making a table of coordinates. - $f(x)=\left(\frac{1}{3}\right)^{x}$ $Graph the function by making a table of coordinates. - f(x)=\left(\frac{1}{3}\right)^{x}$

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $10 ^ { \mathrm { x } } = 2.92$

Evaluate or simplify the expression without using a calculator. - $7 \left( 10 ^ { \log 5.6 } \right)$

Use Compound Interest Formulas Use the compound interest formulas A $A = P \left( 1 + \frac { r } { n } \right) \text { and } A = P e ^ { r t } \text { to solve }$ -Find the accumulated value of an investment of $2000 at 10% compounded semiannually for 7 years.

Model Exponential Growth and Decay Solve. -The half-life of silicon-32 is 710 years. If 30 grams is present now, how much will be present in 300 years? (Round your answer to three decimal places.)

Use the One-to-One Property of Logarithms to Solve Logarithmic Equations Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - $\log x + \log ( x - 1 ) = \log 6$

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $\frac { 1 } { 2 } \left( \log _ { 5 } ( r - 9 ) - \log _ { 5 } r \right)$

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences, Induction, and Probability

Filters

Exam 4: Exponential and Logarithmic Functions

Use Natural Logarithms Evaluate or simplify the expression without using a calculator. - ln⁡1e4\ln \frac { 1 } { e ^ { 4 } }lne41​

Evaluate the expression without using a calculator. - 8log⁡8188 ^ { \log _ { 8 } 18 }8log8​18