Question 1

Find the exponential function that satisfies the given conditions.
-Initial value $= 38$, increasing at a rate of $8 \%$ per year

Accepted Answer

A)  $f ( t ) = 38 \cdot 8 ^ { t }$ 
B)  $f ( t ) = 38 \cdot 0.08 \mathrm { t }$ 
C)  $f ( t ) = 38 \cdot 1.08 ^ { t }$ 
D)  $f ( t ) = 8 \cdot 1.08 ^ { t }$ 
A)  $f ( t ) = 38 \cdot 8 ^ { t }$ 
B)  $f ( t ) = 38 \cdot 0.08 \mathrm { t }$ 
C)  $f ( t ) = 38 \cdot 1.08 ^ { t }$ 
D)  $f ( t ) = 8 \cdot 1.08 ^ { t }$

Question 2

Provide an appropriate response.
-$$\text { Explain how the graph of } y = 3 ^ { x + 2 } - 5 \text { can be obtained from the graph of } y = 3 ^ { x } \text {. }$$

Accepted Answer

The graph is shifted

Question 3

Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x).
-$$f ( x ) = \ln ( - x ) + 10 ; g ( x ) = \ln x$$

Accepted Answer

A)  Reflect across the $y$-axis and translate 10 units to the right. 
B)  Reflect across the $x$-axis and translate 10 units down. 
C)  Reflect across the $y$-axis and translate 10 units up. 
D)  Reflect across the $x$-axis and translate 10 units to the right. 
A)  Reflect across the $y$-axis and translate 10 units to the right. 
B)  Reflect across the $x$-axis and translate 10 units down. 
C)  Reflect across the $y$-axis and translate 10 units up. 
D)  Reflect across the $x$-axis and translate 10 units to the right.

Question 4

Solve the problem.
-What would your monthly payment be for a 4-year $9000 car loan with an APR of 7.89%?

Accepted Answer

A)  $263.10 
B)  $306.95 
C)  $219.25 
D)  $175.40 
A)  $263.10 
B)  $306.95 
C)  $219.25 
D)  $175.40

Question 5

Find the exact solution to the equation.
-$$3 ( 12 - 3 x ) = 27$$

Accepted Answer

A)  $x = 9$ 
B)  $x = 3$ 
C)  $x = - 3$ 
D)  $x = 4$ 
A)  $x = 9$ 
B)  $x = 3$ 
C)  $x = - 3$ 
D)  $x = 4$

Question 6

Determine the doubling time of the investment.
-$1100 at 7% compounded quarterly

Accepted Answer

A)  19.98 years 
B)  14.98 years 
C)  7.99 years 
D)  9.99 years 
A)  19.98 years 
B)  14.98 years 
C)  7.99 years 
D)  9.99 years

Question 7

Find the domain of the function.
-$$f ( x ) = 3 \log _ { 6 } \left( x ^ { 4 } \right)$$

Accepted Answer

A)  $( 3 , \infty )$ 
B)  $\left( \frac { 9 } { 2 } , \infty \right)$ 
C)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
D)  $( 0 , \infty )$ 
A)  $( 3 , \infty )$ 
B)  $\left( \frac { 9 } { 2 } , \infty \right)$ 
C)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
D)  $( 0 , \infty )$

Question 8

Solve the problem.
-Suppose you contribute $75 per quarter into a fund that earns 14.4% annual interest. What is the value of your investment after 12 years?

Accepted Answer

A)  $12,081.74 
B)  $7434.92 
C)  $9293.65 
D)  $16,728.57 
A)  $12,081.74 
B)  $7434.92 
C)  $9293.65 
D)  $16,728.57

Question 9

Solve the problem.
-Find the annual percentage yield if $P is invested at 5.27% compounded continuously.

Accepted Answer

A)  9.47 % 
B)  8.12 % 
C)  6.76 % 
D)  5.41 % 
A)  9.47 % 
B)  8.12 % 
C)  6.76 % 
D)  5.41 %

Question 10

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.
-$\log _ { b } x + \log _ { b } y$

Accepted Answer

A)  $\log _ { b } ( x + y )$ 
B)  $\log _ { 2 b } ( x + y )$ 
C)  $\log _ { b } x y$ 
D)  $\log _ { 2 b } x y$ 
A)  $\log _ { b } ( x + y )$ 
B)  $\log _ { 2 b } ( x + y )$ 
C)  $\log _ { b } x y$ 
D)  $\log _ { 2 b } x y$

Question 11

Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x).
-$$f ( x ) = \ln ( 8 - x ) ; \quad g ( x ) = \ln x$$

Accepted Answer

A)  Reflect across the $y$-axis and then translate 8 units to the left. 
B)  Reflect across the $x$-axis and then translate 8 units to the left. 
C)  Reflect across the $y$-axis and then translate 8 units to the right. 
D)  Reflect across the $x$-axis and then translate 8 units to the right. 
A)  Reflect across the $y$-axis and then translate 8 units to the left. 
B)  Reflect across the $x$-axis and then translate 8 units to the left. 
C)  Reflect across the $y$-axis and then translate 8 units to the right. 
D)  Reflect across the $x$-axis and then translate 8 units to the right.

Question 12

Describe how to transform the graph of g(x) = ln x into the graph of the given function. Graph the function.
-$f(x)=\log _{1 / 8} x$

Accepted Answer

A)  Vertically shrink by a factor $\frac { 1 } { \ln 8 }$
  
B)  Reflect across the $x$-axis and shift up $( \ln 8 )$ units
  
C)  Shift down $( \ln 8 )$ units
  
D)  Reflect across the $x$-axis and $\text { vertically shrink by a factor } \frac{1}{\ln 8}$
  
A)  Vertically shrink by a factor $\frac { 1 } { \ln 8 }$
  
B)  Reflect across the $x$-axis and shift up $( \ln 8 )$ units
  
C)  Shift down $( \ln 8 )$ units
  
D)  Reflect across the $x$-axis and $\text { vertically shrink by a factor } \frac{1}{\ln 8}$

Question 13

Solve the inequality graphically.
-$$5 ^ { - x } < 8 ^ { - x }$$

Accepted Answer

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

Question 14

Find the logistic function that satisfies the given conditions.
-

Accepted Answer

A)  $f ( x ) = 1.8 \cdot 0.9 x$ 
B)  $f ( x ) = 2 \cdot 0.9 x$ 
C)  $f ( x ) = 2 \cdot 0.7 ^ { x }$ 
D)  $f ( x ) = 2 \cdot 1.1 ^ { x }$ 
A)  $f ( x ) = 1.8 \cdot 0.9 x$ 
B)  $f ( x ) = 2 \cdot 0.9 x$ 
C)  $f ( x ) = 2 \cdot 0.7 ^ { x }$ 
D)  $f ( x ) = 2 \cdot 1.1 ^ { x }$

Question 15

Solve the inequality graphically.
-$\left( \frac { 1 } { 8 } \right) ^ { x } < \left( \frac { 1 } { 7 } \right) ^ { x }$

Accepted Answer

A) x 1\) C) $x > 0$ D) $x < 1$ A) x 1\) C) $x > 0$ D) $x < 1$

Question 16

Match the function with its graph.
-f(x) = ln x - ln(x - 2)

Accepted Answer

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

Question 17

Decide if the function is an exponential function. If it is, state the initial value and the base.
-$$y = 9 ^ { 3 }$$

Accepted Answer

A)  Exponential Function; base $= 9$; initial value $= 0$ 
B)  Exponential Function; base $= 3$; initial value $= 0$ 
C)  Not an exponential function 
D)  Exponential Function; base $= 9$; initial value $= 1$ 
A)  Exponential Function; base $= 9$; initial value $= 0$ 
B)  Exponential Function; base $= 3$; initial value $= 0$ 
C)  Not an exponential function 
D)  Exponential Function; base $= 9$; initial value $= 1$

Question 18

Solve the problem.
-Find the future value accumulated in an annuity after investing periodic payments of $300 for 6 years at an annual interest rate of 7%, with payments made and credited 4 times per year.

Accepted Answer

A)  $8853.30 
B)  $15,935.95 
C)  $10,623.97 
D)  $5311.98 
A)  $8853.30 
B)  $15,935.95 
C)  $10,623.97 
D)  $5311.98

Question 19

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry,
boundedness, extrema, asymptotes, and end behavior.
-$$f ( x ) = \frac { 8 } { 1 + 3 e ^ { - x } }$$

Accepted Answer

@#IMG-DLM&
The domain is all real numbers, and the

Question 20

Match the function with its graph.
-$$f ( x ) = \ln x ^ { 3 }$$

Accepted Answer

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

Find the exponential function that satisfies the given conditions. -Initial value $= 38$ , increasing at a rate of $8 \%$ per year

Provide an appropriate response. - $\text { Explain how the graph of } y = 3 ^ { x + 2 } - 5 \text { can be obtained from the graph of } y = 3 ^ { x } \text {. }$

Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x). - $f ( x ) = \ln ( - x ) + 10 ; g ( x ) = \ln x$

Solve the problem. -What would your monthly payment be for a 4-year $9000 car loan with an APR of 7.89%?

Find the exact solution to the equation. - $3 ( 12 - 3 x ) = 27$

Determine the doubling time of the investment. -$1100 at 7% compounded quarterly

Find the domain of the function. - $f ( x ) = 3 \log _ { 6 } \left( x ^ { 4 } \right)$

Solve the problem. -Suppose you contribute $75 per quarter into a fund that earns 14.4% annual interest. What is the value of your investment after 12 years?

Solve the problem. -Find the annual percentage yield if $P is invested at 5.27% compounded continuously.

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. - $\log _ { b } x + \log _ { b } y$

Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x). - $f ( x ) = \ln ( 8 - x ) ; \quad g ( x ) = \ln x$

Describe how to transform the graph of g(x) = ln x into the graph of the given function. Graph the function. - $f(x)=\log _{1 / 8} x$ $Describe how to transform the graph of g(x) = ln x into the graph of the given function. Graph the function. - f(x)=\log _{1 / 8} x$

Solve the inequality graphically. - $5 ^ { - x } < 8 ^ { - x }$

Find the logistic function that satisfies the given conditions. -

Solve the inequality graphically. - $\left( \frac { 1 } { 8 } \right) ^ { x } < \left( \frac { 1 } { 7 } \right) ^ { x }$

Match the function with its graph. -f(x) = ln x - ln(x - 2)

Decide if the function is an exponential function. If it is, state the initial value and the base. - $y = 9 ^ { 3 }$

Solve the problem. -Find the future value accumulated in an annuity after investing periodic payments of $300 for 6 years at an annual interest rate of 7%, with payments made and credited 4 times per year.

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. - $f ( x ) = \frac { 8 } { 1 + 3 e ^ { - x } }$

Match the function with its graph. - $f ( x ) = \ln x ^ { 3 }$

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

Find the exponential function that satisfies the given conditions. -Initial value =38= 38=38 , increasing at a rate of 8%8 \%8% per year

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)+10;g(x)=ln⁡xf ( x ) = \ln ( - x ) + 10 ; g ( x ) = \ln xf(x)=ln(−x)+10;g(x)=lnx