Question 1

Find the following using a calculator. Round to four decimal places.
-$\log ( - 7 )$

Accepted Answer

A)  $2.0794$ 
B)  6 
C)  $1.9459$ 
D)  undefined 
A)  $2.0794$ 
B)  6 
C)  $1.9459$ 
D)  undefined D

Question 2

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry,
boundedness, extrema, asymptotes, and end behavior.
-$$f ( x ) = \frac { 4 } { 1 + 3 e ^ { x } }$$

Accepted Answer

The domain is all real numbers, and the range is $( 0,4 )$. The function is continuous and decreasing on its domain. The graph is symmetric about $\left( \ln \frac { 1 } { 3 } , 2 \right)$, but neither even nor odd. It is bounded below and above. There are no local extrema. The horizontal asymptotes are $y = 0$ and $y = 4$. The end behavior is described by $\lim _ { x \rightarrow \infty } f ( x ) = 4$ and $\lim _ { x \rightarrow\infty } f ( x ) = 0$.

Question 3

Find the exact solution to the equation.
-$$2^{ ( 7 - 3 x )} = \frac { 1 } { 4 }$$

Accepted Answer

A)  $x = - 3$ 
B)  $x = 3$ 
C)  $x = \frac { 1 } { 2 }$ 
D)  $x = 1$ 
A)  $x = - 3$ 
B)  $x = 3$ 
C)  $x = \frac { 1 } { 2 }$ 
D)  $x = 1$ B

Question 4

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

Accepted Answer

A)  Moved right 6 units
  
B)  Moved up 6 units
  
C)  Moved down 6 units
  
D)  Moved left 6 units
  
A)  Moved right 6 units
  
B)  Moved up 6 units
  
C)  Moved down 6 units
  
D)  Moved left 6 units

Question 5

Evaluate the logarithm.
-$$\ln \frac { 1 } { \sqrt { \mathrm { e } ^ { 11 } } }$$

Accepted Answer

A)  $- 22$ 
B)  $- \frac { 11 } { 2 }$ 
C)  $- 11$ 
D)  $\frac { 11 } { 2 }$ 
A)  $- 22$ 
B)  $- \frac { 11 } { 2 }$ 
C)  $- 11$ 
D)  $\frac { 11 } { 2 }$

Question 6

Find the following using a calculator. Round to four decimal places.
-$\ln 31$

Accepted Answer

A)  $3.4657$ 
B)  $3.434$ 
C)  $3.5835$ 
D)  $3.4012$ 
A)  $3.4657$ 
B)  $3.434$ 
C)  $3.5835$ 
D)  $3.4012$

Question 7

Graph the function. Describe its position relative to the graph of the indicated basic function.
-$$f ( x ) = e ^ { 7 x } \text {; relative to } f ( x ) = e ^ { x }$$

Accepted Answer

A)  Shrunk vertically
  
B)  Shrunk horizontally
  
C)  Shrunk horizontally
  
D)  Shrunk vertically
  
A)  Shrunk vertically
  
B)  Shrunk horizontally
  
C)  Shrunk horizontally
  
D)  Shrunk vertically

Question 8

Choose the graph which matches the function.
-$$f ( x ) = - x ^ { 3 }$$

Accepted Answer

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

Question 9

Determine a formula for the exponential function.
-The indicated point is $\left( 0 , \mathrm { e } ^ { 2 } \right)$. Which of the following is the correct equation of the function?

Accepted Answer

A)  $y = e ^ { x + 2 }$. 
B)  $y = e ^ { x } - 2$ 
C)  $y = e ^ { x + 2 }$ 
D)  $y = e ^ { x - 2 }$ 
A)  $y = e ^ { x + 2 }$. 
B)  $y = e ^ { x } - 2$ 
C)  $y = e ^ { x + 2 }$ 
D)  $y = e ^ { x - 2 }$

Question 10

Solve the problem.
-The population of wolves in a state park after $\mathrm { t }$ years is modeled by the function $\mathrm { P } ( \mathrm { t } ) = \frac { 500 } { 1 + 99 \mathrm { e } ^ { - 0.3 \mathrm { t } } }$. What is the maximum number of wolves possible in the park?

Accepted Answer

A)  5 
B)  1000 
C)  99 
D)  500 
A)  5 
B)  1000 
C)  99 
D)  500

Question 11

Solve the equation.
-$$16 ^ { x } = 2$$

Accepted Answer

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

Question 12

Choose the graph which matches the function.
-$f ( x ) = e ^ { 1 } - x ^ { 2 }$

Accepted Answer

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

Question 13

Decide whether the function is an exponential growth or exponential decay function and find the constant percentage
rate of growth or decay.
-$$f ( x ) = 2061 \cdot 0.9928 ^ { x }$$

Accepted Answer

A)  Exponential growth function; $0.0072 \%$ 
B)  Exponential growth function; $- 0.72 \%$ 
C)  Exponential decay function; $- 0.72 \%$ 
D)  Exponential decay function; $0.0072 \%$ 
A)  Exponential growth function; $0.0072 \%$ 
B)  Exponential growth function; $- 0.72 \%$ 
C)  Exponential decay function; $- 0.72 \%$ 
D)  Exponential decay function; $0.0072 \%$

Question 14

Solve the problem.
-A $95,000 mortgage for 30 years at 11% APR requires monthly payments of $904.71. Suppose you decided to make monthly payments of $1,100. How much do you save with the greater payments compared to the original
Plan?

Accepted Answer

A)  $136,605.60 
B)  $96,411.50 
C)  $102,468.40 
D)  $152,591.75 
A)  $136,605.60 
B)  $96,411.50 
C)  $102,468.40 
D)  $152,591.75

Question 15

Provide an appropriate response.
-$$\text { Explain how the graph of } y = 8 \log _ { 2 } x + 5 \text { can be obtained from the graph of } y = \log _ { 2 } x \text {. }$$

Accepted Answer

The graph is stretch

Question 16

Solve the problem.
-Matthew obtains a 25-year $140,000 house loan with an APR of 8.88%. What is his monthly payment?

Accepted Answer

A)  $930.71 
B)  $1396.07 
C)  $1628.75 
D)  $1163.39 
A)  $930.71 
B)  $1396.07 
C)  $1628.75 
D)  $1163.39

Question 17

Assuming all variables are positive, use properties of logarithms to write the expression as a sum or difference of
logarithms or multiples of logarithms.
-$\log _ { 15 } \left( \frac { 14 \sqrt { \mathrm { r } } } { \mathrm { s } } \right)$

Accepted Answer

A)  $\log _ { 15 } ( 14 \sqrt { \mathrm { r } } ) - \log _ { 15 } \mathrm {~s}$ 
B)  $\log _ { 15 } 14 + \frac { 1 } { 2 } \log _ { 15 } \mathrm { r } - \log _ { 15 } \mathrm {~s}$ 
C)  $\log _ { 15 } 14 \cdot \frac { 1 } { 2 } \log _ { 15 } \mathrm { r } \div \log _ { 15 } \mathrm {~s}$ 
D)  $\log _ { 15 } s - \log _ { 15 } 14 - \frac { 1 } { 2 } \log _ { 15 } r$ 
A)  $\log _ { 15 } ( 14 \sqrt { \mathrm { r } } ) - \log _ { 15 } \mathrm {~s}$ 
B)  $\log _ { 15 } 14 + \frac { 1 } { 2 } \log _ { 15 } \mathrm { r } - \log _ { 15 } \mathrm {~s}$ 
C)  $\log _ { 15 } 14 \cdot \frac { 1 } { 2 } \log _ { 15 } \mathrm { r } \div \log _ { 15 } \mathrm {~s}$ 
D)  $\log _ { 15 } s - \log _ { 15 } 14 - \frac { 1 } { 2 } \log _ { 15 } r$

Question 18

Solve the problem.
-Suppose the algae growth in Black Oak Lake increased from 100 cells per milliliter to approximately $10,000,000$ cells per milliliter in a 6-day period. The specific growth rate $\mathrm { r }$ is defined by $\mathrm { r } = \frac { \log \mathrm { N } _ { 2 } - \log _ { 1 } \mathrm {~N} _ { 1 } } { \mathrm { x } _ { 2 } - \mathrm { x } _ { 1 } }$, where $\mathrm { N } _ { 1 }$ is the algae concentration at time $x _ { 1 }$ and $N _ { 2 }$ is the algae concentration at time $x _ { 2 }$. In this situation, what is the specific growth rate of algae? Round your results to the nearest hundredth.

Accepted Answer

A)  $1,666,650.00$ 
B)  $- 1,666,650.00$ 
C)  $0.83$ 
D)  $- 0.83$ 
A)  $1,666,650.00$ 
B)  $- 1,666,650.00$ 
C)  $0.83$ 
D)  $- 0.83$

Question 19

Find the amount accumulated after investing a principal P for t years at an interest rate r.
-P = $14,000, t = 14, r = 8%, compounded semiannually (k = 2)

Accepted Answer

A)  $41,981.85 
B)  $41,120.71 
C)  $27,981.85 
D)  $40,367.16 
A)  $41,981.85 
B)  $41,120.71 
C)  $27,981.85 
D)  $40,367.16

Question 20

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

Accepted Answer

A)  Shrunk vertically
  
B)  Stretched horizontally
  
C)  Moved up 3 units
  
D)  Stretched vertically
  
A)  Shrunk vertically
  
B)  Stretched horizontally
  
C)  Moved up 3 units
  
D)  Stretched vertically

Find the following using a calculator. Round to four decimal places. - $\log ( - 7 )$

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. - $f ( x ) = \frac { 4 } { 1 + 3 e ^ { x } }$

Find the exact solution to the equation. - $2^{ ( 7 - 3 x )} = \frac { 1 } { 4 }$

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

Evaluate the logarithm. - $\ln \frac { 1 } { \sqrt { \mathrm { e } ^ { 11 } } }$

Find the following using a calculator. Round to four decimal places. - $\ln 31$

Choose the graph which matches the function. - $f ( x ) = - x ^ { 3 }$ $Choose the graph which matches the function. - f ( x ) = - x ^ { 3 }$

Solve the problem. -The population of wolves in a state park after $\mathrm { t }$ years is modeled by the function $\mathrm { P } ( \mathrm { t } ) = \frac { 500 } { 1 + 99 \mathrm { e } ^ { - 0.3 \mathrm { t } } }$ . What is the maximum number of wolves possible in the park?

Solve the equation. - $16 ^ { x } = 2$

Choose the graph which matches the function. - $f ( x ) = e ^ { 1 } - x ^ { 2 }$ $Choose the graph which matches the function. - f ( x ) = e ^ { 1 } - x ^ { 2 }$

Decide whether the function is an exponential growth or exponential decay function and find the constant percentage rate of growth or decay. - $f ( x ) = 2061 \cdot 0.9928 ^ { x }$

Solve the problem. -A $95,000 mortgage for 30 years at 11% APR requires monthly payments of $904.71. Suppose you decided to make monthly payments of $1,100. How much do you save with the greater payments compared to the original Plan?

Provide an appropriate response. - $\text { Explain how the graph of } y = 8 \log _ { 2 } x + 5 \text { can be obtained from the graph of } y = \log _ { 2 } x \text {. }$

Solve the problem. -Matthew obtains a 25-year $140,000 house loan with an APR of 8.88%. What is his monthly payment?

Assuming all variables are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. - $\log _ { 15 } \left( \frac { 14 \sqrt { \mathrm { r } } } { \mathrm { s } } \right)$

Find the amount accumulated after investing a principal P for t years at an interest rate r. -P = $14,000, t = 14, r = 8%, compounded semiannually (k = 2)

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 following using a calculator. Round to four decimal places. - log⁡(−7)\log ( - 7 )log(−7)

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. - f(x)=41+3exf ( x ) = \frac { 4 } { 1 + 3 e ^ { x } }f(x)=1+3ex4​

Find the exact solution to the equation. - 2(7−3x)=142^{ ( 7 - 3 x )} = \frac { 1 } { 4 }2(7−3x)=41​

Graph the function. Describe its position relative to the graph of the indicated basic function. - f(x)=ln⁡x+6; relative to f(x)=ln⁡xf(x)=\ln x+6 \text {; relative to } f(x)=\ln xf(x)=lnx+6; relative to f(x)=lnx

Evaluate the logarithm. - ln⁡1e11\ln \frac { 1 } { \sqrt { \mathrm { e } ^ { 11 } } }lne11​1​

Find the following using a calculator. Round to four decimal places. - ln⁡31\ln 31ln31

Graph the function. Describe its position relative to the graph of the indicated basic function. - f(x)=e7x; relative to f(x)=exf ( x ) = e ^ { 7 x } \text {; relative to } f ( x ) = e ^ { x }f(x)=e7x; relative to f(x)=ex

Choose the graph which matches the function. - f(x)=−x3f ( x ) = - x ^ { 3 }f(x)=−x3

Determine a formula for the exponential function. -The indicated point is (0,e2)\left( 0 , \mathrm { e } ^ { 2 } \right)(0,e2) . Which of the following is the correct equation of the function?

Solve the equation. - 16x=216 ^ { x } = 216x=2

Choose the graph which matches the function. - f(x)=e1−x2f ( x ) = e ^ { 1 } - x ^ { 2 }f(x)=e1−x2

Decide whether the function is an exponential growth or exponential decay function and find the constant percentage rate of growth or decay. - f(x)=2061⋅0.9928xf ( x ) = 2061 \cdot 0.9928 ^ { x }f(x)=2061⋅0.9928x