Question 1

Use transformations to graph the function.
-$f(x)=e^{x-5}$

Accepted Answer

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

Question 2

Find the domain of the function.
-$$f ( x ) = \log ( x - 9 )$$

Accepted Answer

A)  $( 0 , \infty )$ 
B)  $( 9 , \infty )$ 
C)  $( - 9 , \infty )$ 
D)  $( 1 , \infty )$ 
A)  $( 0 , \infty )$ 
B)  $( 9 , \infty )$ 
C)  $( - 9 , \infty )$ 
D)  $( 1 , \infty )$

Question 3

Solve the problem.
-The half-life of silicon-32 is 710 years. If 60 grams is present now, how much will be present in 300 years? (Round your answer to three decimal places.)

Accepted Answer

A) 58.268 
B) 3.208 
C) 0 
D) 44.767 
A) 58.268 
B) 3.208 
C) 0 
D) 44.767

Question 4

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
-$\log _ { 2 } \sqrt [ 5 ] { y }$

Accepted Answer

A)  $\frac { 1 } { 5 } \log _ { 2 } y$ 
B)  $\frac { 1 } { 2 } \log _ { 5 } y$ 
C)  $5 \log _ { 2 } y$ 
D)  $\frac { 1 } { 5 } \log _ { 2 } \sqrt [ 5 ] { y }$ 
A)  $\frac { 1 } { 5 } \log _ { 2 } y$ 
B)  $\frac { 1 } { 2 } \log _ { 5 } y$ 
C)  $5 \log _ { 2 } y$ 
D)  $\frac { 1 } { 5 } \log _ { 2 } \sqrt [ 5 ] { y }$

Question 5

Solve the problem.
-A city is growing at the rate of 0.9% annually. If there were 5,400,000 residents in the city in 1992, find how many (to the nearest ten-thousand)were living in that city in 2000. $$\text { Use } y = 5,400,000 ( 2.7 ) ^ { 0.009 t }$$

Accepted Answer

A) 14,580,000 
B) 5,800,000 
C) 5,830,000 
D) 1,050,000 
A) 14,580,000 
B) 5,800,000 
C) 5,830,000 
D) 1,050,000

Question 6

Evaluate the logarithm without the use of a calculator.
-$$\log _ { 9 } \frac { 1 } { 81 }$$

Accepted Answer

A) 9 
B) -2 
C) 2 
D) -9 
A) 9 
B) -2 
C) 2 
D) -9

Question 7

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
-$\log _ { 4 } \sqrt { 11 x }$

Accepted Answer

A)  $\frac { 1 } { 2 } \log _ { 4 } 11 + \frac { 1 } { 2 } \log _ { 4 } x$ 
B)  $\log _ { 4 } \sqrt { 11 } + \log _ { 4 } \sqrt { x }$ 
C)  $\log _ { 4 } 11 + \frac { 1 } { 2 } \log _ { 4 } x$ 
D)  $\frac { 1 } { 2 } \log _ { 4 } 11 x$ 
A)  $\frac { 1 } { 2 } \log _ { 4 } 11 + \frac { 1 } { 2 } \log _ { 4 } x$ 
B)  $\log _ { 4 } \sqrt { 11 } + \log _ { 4 } \sqrt { x }$ 
C)  $\log _ { 4 } 11 + \frac { 1 } { 2 } \log _ { 4 } x$ 
D)  $\frac { 1 } { 2 } \log _ { 4 } 11 x$

Question 8

Evaluate the logarithm without the use of a calculator.
-$\log _ { 7 } \sqrt { 7 }$

Accepted Answer

A)  7 
B)  $\frac { 1 } { 7 }$ 
C)  $\frac { 1 } { 2 }$ 
D)  1 
A)  7 
B)  $\frac { 1 } { 7 }$ 
C)  $\frac { 1 } { 2 }$ 
D)  1

Question 9

Solve the problem.
-$$P ( t ) = \frac { 360 } { 1 + 35 e ^ { - 0.181 t } }$$ territory after t years. What will the population be in 30 years?

Accepted Answer

A) 360 
B) 2347 
C) 319 
D) 312 
A) 360 
B) 2347 
C) 319 
D) 312

Question 10

Find the domain of the function.
-$$f ( x ) = \log _ { 5 } \left( 25 - x ^ { 2 } \right)$$

Accepted Answer

A)  $( \infty , - 5 ) \cup ( 5 , \infty )$ 
B)  $( - 5,5 )$ 
C)  $[ - 5,5 ]$ 
D)  $( - 25,25 )$ 
A)  $( \infty , - 5 ) \cup ( 5 , \infty )$ 
B)  $( - 5,5 )$ 
C)  $[ - 5,5 ]$ 
D)  $( - 25,25 )$

Question 11

Use transformations to graph the function.
-$f(x)=2^{-x}-4$

Accepted Answer

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

Question 12

Solve the equation.
-$$e ^ { 4 x - 1 } = \left( e ^ { 6 } \right) ^ { - x }$$

Accepted Answer

A)  $\{ 0 \}$ 
B)  $\left\{ \frac { 7 } { 5 } \right\}$ 
C)  $\left\{ \frac { 1 } { 10 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 2 } \right\}$ 
A)  $\{ 0 \}$ 
B)  $\left\{ \frac { 7 } { 5 } \right\}$ 
C)  $\left\{ \frac { 1 } { 10 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 2 } \right\}$

Question 13

Solve the problem.
-Which has a lower present value: $30,000 if interest is paid at a rate of 5.98% compounded continuously for 5 years, or $33,000 if interest is paid at a rate of 3.3% compounded continuously for 65 months?

Accepted Answer

A) $33,000 with interest is paid at a rate of 3.3% compounded continuously for 65 months has a lower present value. 
B) $30,000 with interest paid at a rate of 5.98% compounded continuously for 5 years has a lower present value. 
C) Both investments have the same present value. 
A) $33,000 with interest is paid at a rate of 3.3% compounded continuously for 65 months has a lower present value. 
B) $30,000 with interest paid at a rate of 5.98% compounded continuously for 5 years has a lower present value. 
C) Both investments have the same present value.

Question 14

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the
solution.
-$$\left( \frac { 1 } { 4 } \right) ^ { x } = 18$$

Accepted Answer

A)  $\{ 2.08 \}$ 
B)  $\{ - 4.50 \}$ 
C)  $\{ - 2.08 \}$ 
D)  $\{ - 0.48 \}$ 
A)  $\{ 2.08 \}$ 
B)  $\{ - 4.50 \}$ 
C)  $\{ - 2.08 \}$ 
D)  $\{ - 0.48 \}$

Question 15

Solve the problem.
-How long will it take for an investment to double in value if it earns 4.25% compounded continuously? Round your answer to three decimal places.

Accepted Answer

A) 25.85 yr 
B) 16.309 yr 
C) 8.155 yr 
D) 17.715 yr 
A) 25.85 yr 
B) 16.309 yr 
C) 8.155 yr 
D) 17.715 yr

Question 16

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
-$\ln \sqrt [ 6 ] { \mathrm { ey } }$

Accepted Answer

A)  $6 \ln y + 6$ 
B)  $\frac { 1 } { 6 } \ln y + \frac { 1 } { 6 }$ 
C)  $\frac { 1 } { 6 } \ln \sqrt [ 6 ] { \mathrm { ey } } + \frac { 1 } { 6 }$ 
D)  $\frac { y } { 6 }$ 
A)  $6 \ln y + 6$ 
B)  $\frac { 1 } { 6 } \ln y + \frac { 1 } { 6 }$ 
C)  $\frac { 1 } { 6 } \ln \sqrt [ 6 ] { \mathrm { ey } } + \frac { 1 } { 6 }$ 
D)  $\frac { y } { 6 }$

Question 17

Evaluate the logarithm without the use of a calculator.
-$$\log _ { 3 } 1$$

Accepted Answer

A) 1 
B) $\frac { 1 } { 3 }$ 
C) 0 
D) 3 
A) 1 
B) $\frac { 1 } { 3 }$ 
C) 0 
D) 3

Question 18

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.
-$2 \log _ { b } m - \log _ { b } n$

Accepted Answer

A)  $\log _ { \mathrm { b } } \left( \frac { \mathrm { m } ^ { 2 } } { \mathrm { n } } \right)$ 
B)  $\log _ { \mathrm { b } } \mathrm { m } ^ { 2 } \div \log _ { \mathrm { b } } \mathrm { n }$ 
C)  $\log _ { b } \left( \frac { 2 m } { n } \right)$ 
D)  $\log _ { \mathrm { b } } \left( \mathrm { m } ^ { 2 } - \mathrm { n } \right)$ 
A)  $\log _ { \mathrm { b } } \left( \frac { \mathrm { m } ^ { 2 } } { \mathrm { n } } \right)$ 
B)  $\log _ { \mathrm { b } } \mathrm { m } ^ { 2 } \div \log _ { \mathrm { b } } \mathrm { n }$ 
C)  $\log _ { b } \left( \frac { 2 m } { n } \right)$ 
D)  $\log _ { \mathrm { b } } \left( \mathrm { m } ^ { 2 } - \mathrm { n } \right)$

Question 19

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the
solution.
-$$e ^ { x + 4 } = 2$$

Accepted Answer

A)  $\{ - 2.21 \}$ 
B)  $\{ - 3.08 \}$ 
C)  $\{ 1.79 \}$ 
D)  $\{ - 3.31 \}$ 
A)  $\{ - 2.21 \}$ 
B)  $\{ - 3.08 \}$ 
C)  $\{ 1.79 \}$ 
D)  $\{ - 3.31 \}$

Question 20

Write the exponential equation as an equation involving a logarithm.
-$$4 ^ { - 2 } = \frac { 1 } { 16 }$$

Accepted Answer

A)  $\log _ { 4 } \frac { 1 } { 16 } = - 2$ 
B)  $\log _ { 1 / 16 } 4 = - 2$ 
C)  $\log _ { 4 } - 2 = \frac { 1 } { 16 }$ 
D)  $\log _ { - 2 } \frac { 1 } { 16 } = 4$ 
A)  $\log _ { 4 } \frac { 1 } { 16 } = - 2$ 
B)  $\log _ { 1 / 16 } 4 = - 2$ 
C)  $\log _ { 4 } - 2 = \frac { 1 } { 16 }$ 
D)  $\log _ { - 2 } \frac { 1 } { 16 } = 4$

Use transformations to graph the function. - $f(x)=e^{x-5}$ $Use transformations to graph the function. - f(x)=e^{x-5}$

Find the domain of the function. - $f ( x ) = \log ( x - 9 )$

Solve the problem. -The half-life of silicon-32 is 710 years. If 60 grams is present now, how much will be present in 300 years? (Round your answer to three decimal places.)

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 2 } \sqrt [ 5 ] { y }$

Solve the problem. -A city is growing at the rate of 0.9% annually. If there were 5,400,000 residents in the city in 1992, find how many (to the nearest ten-thousand)were living in that city in 2000. $\text { Use } y = 5,400,000 ( 2.7 ) ^ { 0.009 t }$

Evaluate the logarithm without the use of a calculator. - $\log _ { 9 } \frac { 1 } { 81 }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 4 } \sqrt { 11 x }$

Evaluate the logarithm without the use of a calculator. - $\log _ { 7 } \sqrt { 7 }$

Solve the problem. - $P ( t ) = \frac { 360 } { 1 + 35 e ^ { - 0.181 t } }$ territory after t years. What will the population be in 30 years?

Find the domain of the function. - $f ( x ) = \log _ { 5 } \left( 25 - x ^ { 2 } \right)$

Use transformations to graph the function. - $f(x)=2^{-x}-4$ $Use transformations to graph the function. - f(x)=2^{-x}-4$

Solve the equation. - $e ^ { 4 x - 1 } = \left( e ^ { 6 } \right) ^ { - x }$

Solve the problem. -Which has a lower present value: $30,000 if interest is paid at a rate of 5.98% compounded continuously for 5 years, or $33,000 if interest is paid at a rate of 3.3% compounded continuously for 65 months?

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $\left( \frac { 1 } { 4 } \right) ^ { x } = 18$

Solve the problem. -How long will it take for an investment to double in value if it earns 4.25% compounded continuously? Round your answer to three decimal places.

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\ln \sqrt [ 6 ] { \mathrm { ey } }$

Evaluate the logarithm without the use of a calculator. - $\log _ { 3 } 1$

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. - $2 \log _ { b } m - \log _ { b } n$

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $e ^ { x + 4 } = 2$

Write the exponential equation as an equation involving a logarithm. - $4 ^ { - 2 } = \frac { 1 } { 16 }$

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Exam 5: Exponential and Logarithmic Functions and Equations

Use transformations to graph the function. - f(x)=ex−5f(x)=e^{x-5}f(x)=ex−5

Find the domain of the function. - f(x)=log⁡(x−9)f ( x ) = \log ( x - 9 )f(x)=log(x−9)

Solve the problem. -The half-life of silicon-32 is 710 years. If 60 grams is present now, how much will be present in 300 years? (Round your answer to three decimal places.)

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡2y5\log _ { 2 } \sqrt [ 5 ] { y }log2​5y​

Evaluate the logarithm without the use of a calculator. - log⁡9181\log _ { 9 } \frac { 1 } { 81 }log9​811​

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡411x\log _ { 4 } \sqrt { 11 x }log4​11x​

Evaluate the logarithm without the use of a calculator. - log⁡77\log _ { 7 } \sqrt { 7 }log7​7​

Solve the problem. - P(t)=3601+35e−0.181tP ( t ) = \frac { 360 } { 1 + 35 e ^ { - 0.181 t } }P(t)=1+35e−0.181t360​ territory after t years. What will the population be in 30 years?

Find the domain of the function. - f(x)=log⁡5(25−x2)f ( x ) = \log _ { 5 } \left( 25 - x ^ { 2 } \right)f(x)=log5​(25−x2)

Use transformations to graph the function. - f(x)=2−x−4f(x)=2^{-x}-4f(x)=2−x−4

Solve the equation. - e4x−1=(e6)−xe ^ { 4 x - 1 } = \left( e ^ { 6 } \right) ^ { - x }e4x−1=(e6)−x