Question 1

Provide an appropriate response.
-Explain how the graph of y = -log3 (-x) can be obtained from the graph of y = log3 x.

Accepted Answer

The graph is reflect

Question 2

Find the domain of the function.
-$$f ( x ) = \log _ { 4 } ( 3 x + 4 )$$

Accepted Answer

A)  $\left( - \frac { 4 } { 3 } , \infty \right)$ 
B)  $( 0 , \infty )$ 
C)  $\left[ - \frac { 4 } { 3 } , \infty \right)$ 
D)  $\left( \frac { 4 } { 3 } , \infty \right)$ 
A)  $\left( - \frac { 4 } { 3 } , \infty \right)$ 
B)  $( 0 , \infty )$ 
C)  $\left[ - \frac { 4 } { 3 } , \infty \right)$ 
D)  $\left( \frac { 4 } { 3 } , \infty \right)$

Question 3

Solve the problem.
-Use the formula $\beta = 10 \log \left( \mathrm { I } / \mathrm { I } _ { \mathrm { O } } \right)$, where the loudness of a sound in decibels is determined by $\mathrm { I }$, the number of Watts/ $/ \mathrm { m } ^ { 2 }$ produced by the sound wave, and $\mathrm { I } _ { \mathrm { O } } = 10 ^ { - 12 } \mathrm {~W} / \mathrm { m } ^ { 2 }$. What is the intensity in Watts/m² of a noise measured at 37 decibels? (Round to the nearest tenth.)

Accepted Answer

A)  $4.0 \times 10^{13} \mathrm {~W} / \mathrm { m } ^ { 2 }$ 
B)  $5.0 \times 10 ^ { - 9 } \mathrm {~W} / \mathrm { m } ^ { 2 }$ 
C)  $5.0 \times 10 ^ { - 8 } \mathrm {~W} / \mathrm { m } ^ { 2 }$ 
D)  $3.7 \times 10 ^ { - 10 } \mathrm {~W} / \mathrm { m } ^ { 2 }$ 
A)  $4.0 \times 10^{13} \mathrm {~W} / \mathrm { m } ^ { 2 }$ 
B)  $5.0 \times 10 ^ { - 9 } \mathrm {~W} / \mathrm { m } ^ { 2 }$ 
C)  $5.0 \times 10 ^ { - 8 } \mathrm {~W} / \mathrm { m } ^ { 2 }$ 
D)  $3.7 \times 10 ^ { - 10 } \mathrm {~W} / \mathrm { m } ^ { 2 }$

Question 4

Solve the inequality graphically.
-$5 ^ { x } < 2 ^ { x }$

Accepted Answer

A) $x > 1$ B) $x 0$ D) $x < 1$ A) $x > 1$ B) $x 0$ D) $x < 1$

Question 5

Solve the problem.
-A $98,000 mortgage for 30 years at 9% APR requires monthly payments of $788.53. Suppose you decided to make monthly payments of $1,100. When would the mortgage be completely paid?

Accepted Answer

A)  11.07 years 
B)  13.53 years 
C)  9.84 years 
D)  12.30 years 
A)  11.07 years 
B)  13.53 years 
C)  9.84 years 
D)  12.30 years

Question 6

Solve the equation.
-$$\mathrm { e } ^ { \mathrm { x } } + \mathrm { e } ^ { - \mathrm { x } } = 6$$

Accepted Answer

A)  $1.3573 , - 2.1682$ 
B)  $1.7551 , - 1.5319$ 
C)  $1.8184 , - 1.8184$ 
D)  $1.7627 , - 1.7627$ 
A)  $1.3573 , - 2.1682$ 
B)  $1.7551 , - 1.5319$ 
C)  $1.8184 , - 1.8184$ 
D)  $1.7627 , - 1.7627$

Question 7

Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x).
-$$f ( x ) = \ln ( x + 3 ) - 4 ; \quad g ( x ) = \ln x$$

Accepted Answer

A)  Translate 4 units to the left and 3 units up. 
B)  Translate 3 units to the left and 4 units up. 
C)  Translate 3 units to the right and 4 units down. 
D)  Translate 3 units to the left and 4 units down. 
A)  Translate 4 units to the left and 3 units up. 
B)  Translate 3 units to the left and 4 units up. 
C)  Translate 3 units to the right and 4 units down. 
D)  Translate 3 units to the left and 4 units down.

Question 8

Solve the equation.
-$$\left( \frac { 4 } { 5 } \right) ^ { x } = \frac { 25 } { 16 }$$

Accepted Answer

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

Question 9

Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all
variables represent positive real numbers.
-$2 \log x + 5 \log y$

Accepted Answer

A)  $\log \left( x ^ { 2 } y ^ { 5 } \right)$ 
B)  $\log ( 2 x + 5 y )$ 
C)  $\log ( 10 x y )$ 
D)  $\log \left( x ^ { 2 } + y ^ { 5 } \right)$ 
A)  $\log \left( x ^ { 2 } y ^ { 5 } \right)$ 
B)  $\log ( 2 x + 5 y )$ 
C)  $\log ( 10 x y )$ 
D)  $\log \left( x ^ { 2 } + y ^ { 5 } \right)$

Question 10

Solve the equation.
-$$4 ( 7 - 3 x ) = \frac { 1 } { 16 }$$

Accepted Answer

A)  4 
B)  $- 3$ 
C)  3 
D)  $\frac { 1 } { 4 }$ 
A)  4 
B)  $- 3$ 
C)  3 
D)  $\frac { 1 } { 4 }$

Question 11

Determine the doubling time of the investment.
-6.25% APR compounded semiannually

Accepted Answer

A)  16.89 years 
B)  11.26 years 
C)  9.01 years 
D)  22.53 years 
A)  16.89 years 
B)  11.26 years 
C)  9.01 years 
D)  22.53 years

Question 12

Compute the exact value of the function for the given x-value without using a calculator.
-$f ( x ) = 3 ^ { 1 - x }$ for $x = 4$

Accepted Answer

A)  $- 9$ 
B)  27 
C)  $\frac { 1 } { 27 }$ 
D)  $\frac { 1 } { 9 }$ 
A)  $- 9$ 
B)  27 
C)  $\frac { 1 } { 27 }$ 
D)  $\frac { 1 } { 9 }$

Question 13

Find the exact solution to the equation.
-$125 \left( \frac { 1 } { 5 } \right) ^ { x / 3 } = 5$

Accepted Answer

A)  $x = \frac { 2 } { 3 }$ 
B)  $x = 7$ 
C)  $x = 6$ 
D)  $x = 2$ 
A)  $x = \frac { 2 } { 3 }$ 
B)  $x = 7$ 
C)  $x = 6$ 
D)  $x = 2$

Question 14

Graph the function. Describe its position relative to the graph of the indicated basic function.
-$$f ( x ) = e ^ { - x + 6 } ; \text { relative to } f ( x ) = e ^ { x }$$

Accepted Answer

A)  Reflected across the $y$-axis;
moved left 6 units
  
B)  Moved left 6 units;
 reflected across the $y$-axis
  
C)  Moved right 6 units;
 Reflected across the y-axis
  
D) ; reflected across the $y$-axis 
moved right 6 units
  
A)  Reflected across the $y$-axis;
moved left 6 units
  
B)  Moved left 6 units;
 reflected across the $y$-axis
  
C)  Moved right 6 units;
 Reflected across the y-axis
  
D) ; reflected across the $y$-axis 
moved right 6 units

Question 15

Find the logistic function that satisfies the given conditions.
-Initial value $= 4$, limit to growth $= 24$, passing through $( 1,12 )$

Accepted Answer

A)  $f ( x ) = \frac { 12 } { 1 + 6 ( 1 / 5 ) ^ { x } }$ 
B)  $f ( x ) = \frac { 24 } { 1 + 5 ( 1 / 5 ) ^ { x } }$ 
C)  $f ( x ) = \frac { 4 } { 1 + 6 ( 1 / 2 ) ^ { x } }$ 
D)  $f ( x ) = \frac { 24 } { 1 + 5 ( 1 / 10 ) ^ { x } }$ 
A)  $f ( x ) = \frac { 12 } { 1 + 6 ( 1 / 5 ) ^ { x } }$ 
B)  $f ( x ) = \frac { 24 } { 1 + 5 ( 1 / 5 ) ^ { x } }$ 
C)  $f ( x ) = \frac { 4 } { 1 + 6 ( 1 / 2 ) ^ { x } }$ 
D)  $f ( x ) = \frac { 24 } { 1 + 5 ( 1 / 10 ) ^ { x } }$

Question 16

Find the exponential function that satisfies the given conditions.
-Initial population $= 30,991$, increasing at a rate of $2.8 \%$ per year

Accepted Answer

A)  $\mathrm { P } ( \mathrm { t } ) = 30,991 \cdot 1.028 ^ { \mathrm { t } }$ 
B)  $\mathrm { P } ( \mathrm { t } ) = 30,991 \cdot 2.8 ^ { \mathrm { t } }$ 
C)  $\mathrm { P } ( \mathrm { t } ) = 2.8 \cdot 30,991 ^ { \mathrm { t } }$ 
D)  $\mathrm { P } ( \mathrm { t } ) = 30,991 \cdot 0.02 \mathrm { t } ^ { \mathrm { t } }$ 
A)  $\mathrm { P } ( \mathrm { t } ) = 30,991 \cdot 1.028 ^ { \mathrm { t } }$ 
B)  $\mathrm { P } ( \mathrm { t } ) = 30,991 \cdot 2.8 ^ { \mathrm { t } }$ 
C)  $\mathrm { P } ( \mathrm { t } ) = 2.8 \cdot 30,991 ^ { \mathrm { t } }$ 
D)  $\mathrm { P } ( \mathrm { t } ) = 30,991 \cdot 0.02 \mathrm { t } ^ { \mathrm { t } }$

Question 17

Solve the problem.
-How long will it take for prices in the economy to double at a 9% annual inflation rate? (Round to the nearest year.)

Accepted Answer

A)  8 yr 
B)  23 yr 
C)  13 yr 
D)  7 yr 
A)  8 yr 
B)  23 yr 
C)  13 yr 
D)  7 yr

Question 18

Graph the function. Describe its position relative to the graph of the indicated basic function.
-$f(x)=\ln x-3 ; \text { relative to } f(x)=\ln x$

Accepted Answer

A)  Moved up 3 units
  
B)  Moved right 3 units
  
C)  Moved down 3 units
  
D)  Moved down 3 units
  
A)  Moved up 3 units
  
B)  Moved right 3 units
  
C)  Moved down 3 units
  
D)  Moved down 3 units

Question 19

Solve the problem.
-Find the future value accumulated in an annuity after investing periodic payments of $1500 for 13 years at an annual interest rate of 5.5%, with payments made and credited 2 times per year.

Accepted Answer

A)  $67,061.18 
B)  $55,884.31 
C)  $100,591.76 
D)  $33,530.59 
A)  $67,061.18 
B)  $55,884.31 
C)  $100,591.76 
D)  $33,530.59

Question 20

Use a calculator to find an approximate solution to the equation.
-$$6 e ^ { 6 x + 4 } = 12$$

Accepted Answer

A)  $- 0.551$ 
B)  $1.333$ 
C)  $- 0.598$ 
D)  $0.782$ 
A)  $- 0.551$ 
B)  $1.333$ 
C)  $- 0.598$ 
D)  $0.782$

Provide an appropriate response. -Explain how the graph of y = -log3 (-x) can be obtained from the graph of y = log3 x.

Find the domain of the function. - $f ( x ) = \log _ { 4 } ( 3 x + 4 )$

Solve the inequality graphically. - $5 ^ { x } < 2 ^ { x }$

Solve the problem. -A $98,000 mortgage for 30 years at 9% APR requires monthly payments of $788.53. Suppose you decided to make monthly payments of $1,100. When would the mortgage be completely paid?

Solve the equation. - $\mathrm { e } ^ { \mathrm { x } } + \mathrm { e } ^ { - \mathrm { x } } = 6$

Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x). - $f ( x ) = \ln ( x + 3 ) - 4 ; \quad g ( x ) = \ln x$

Solve the equation. - $\left( \frac { 4 } { 5 } \right) ^ { x } = \frac { 25 } { 16 }$

Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all variables represent positive real numbers. - $2 \log x + 5 \log y$

Solve the equation. - $4 ( 7 - 3 x ) = \frac { 1 } { 16 }$

Determine the doubling time of the investment. -6.25% APR compounded semiannually

Compute the exact value of the function for the given x-value without using a calculator. - $f ( x ) = 3 ^ { 1 - x }$ for $x = 4$

Find the exact solution to the equation. - $125 \left( \frac { 1 } { 5 } \right) ^ { x / 3 } = 5$

Find the logistic function that satisfies the given conditions. -Initial value $= 4$ , limit to growth $= 24$ , passing through $( 1,12 )$

Find the exponential function that satisfies the given conditions. -Initial population $= 30,991$ , increasing at a rate of $2.8 \%$ per year

Solve the problem. -How long will it take for prices in the economy to double at a 9% annual inflation rate? (Round to the nearest year.)

Graph the function. Describe its position relative to the graph of the indicated basic function. - $f(x)=\ln x-3 ; \text { relative to } f(x)=\ln x$ $Graph the function. Describe its position relative to the graph of the indicated basic function. - f(x)=\ln x-3 ; \text { relative to } f(x)=\ln x$

Solve the problem. -Find the future value accumulated in an annuity after investing periodic payments of $1500 for 13 years at an annual interest rate of 5.5%, with payments made and credited 2 times per year.

Use a calculator to find an approximate solution to the equation. - $6 e ^ { 6 x + 4 } = 12$

Functions and Graphs

Polynomial, Power, and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 3: Exponential, Logistic, and Logarithmic Functions

Provide an appropriate response. -Explain how the graph of y = -log3 (-x) can be obtained from the graph of y = log3 x.

Find the domain of the function. - f(x)=log⁡4(3x+4)f ( x ) = \log _ { 4 } ( 3 x + 4 )f(x)=log4​(3x+4)

Solve the inequality graphically. - 5x<2x5 ^ { x } < 2 ^ { x }5x<2x