Question 1

Graph the function.
-$f(x)=3 e^{-x}$

Accepted Answer

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

Question 2

Match the equation with its graph.
-$$y = 2 ^ { - x }$$

Accepted Answer

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

Question 3

The number of quarters needed to double an investment when a lump sum is invested at 10%, compounded quarterly, is given b $\mathrm { n } = \frac { \ln 2 } { \ln 1.025 }$ Find n, rounded to the nearest tenth.

Accepted Answer

A)  28.1 quarters 
B)  33.1 quarters 
C)  24.1 quarters 
D)  31.1 quarters 
A)  28.1 quarters 
B)  33.1 quarters 
C)  24.1 quarters 
D)  31.1 quarters

Question 4

Graph the function.
-$f(x)=2^{x}$

Accepted Answer

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

Question 5

Provide an appropriate response.
-If interest is compounded monthly at 5% per year for 14 years, explain how to find the number of compounding
periods and the interest rate per compounding period.

Accepted Answer

The number of compou

Question 6

The decay of 514 mg of an isotope is given by A( $A ( t ) = 514 e ^ { - 0.021 t }$ , where t is time in years. Find the amount left after 63 years.

Accepted Answer

A)  503 mg 
B)  134 mg 
C)  69 mg 
D)  137 mg 
A)  503 mg 
B)  134 mg 
C)  69 mg 
D)  137 mg

Question 7

Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places.
-ln (5 x-2)=ln 12-ln (x-6)

Accepted Answer

A)  $\frac { 32 } { 5 }$ 
B)  0,$\frac { 32 } { 5 }$ 
C)  6 ,$\frac { 6 } { 5 }$ 
D)  no solution 
A)  $\frac { 32 } { 5 }$ 
B)  0,$\frac { 32 } { 5 }$ 
C)  6 ,$\frac { 6 } { 5 }$ 
D)  no solution

Question 8

Find the function value.
-Let $f ( x ) = \left( \frac { 1 } { 6 } \right) ^ { x }$. Find $f ( 3 )$.

Accepted Answer

A)  216 
B)  $\frac { 1 } { 216 }$ 
C)  $\frac { 1 } { 729 }$ 
D)  $\frac { 1 } { 18 }$ 
A)  216 
B)  $\frac { 1 } { 216 }$ 
C)  $\frac { 1 } { 729 }$ 
D)  $\frac { 1 } { 18 }$

Question 9

Find the inverse of the function.
-$$f ( x ) = e ^ { - x } + 2$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = - e ^ { x } - 2$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { e } ^ { \mathrm { x } } - \frac { 1 } { \mathrm {~s} }$ 
C)  $f ^ { - 1 } ( x ) = - \ln ( x - 2 )$ 
D)  $f ^ { - 1 } ( x ) = \ln 2 - \ln x$ 
A)  $f ^ { - 1 } ( x ) = - e ^ { x } - 2$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { e } ^ { \mathrm { x } } - \frac { 1 } { \mathrm {~s} }$ 
C)  $f ^ { - 1 } ( x ) = - \ln ( x - 2 )$ 
D)  $f ^ { - 1 } ( x ) = \ln 2 - \ln x$

Question 10

Provide an appropriate response.
-The following table has the inputs, x, and the outputs for three functions, f, g, and h. Test the percent change of the
outputs to determine which function is exactly exponential, which is approximately exponential, and which is not
exponential. $$\begin{array} { c | c | c | c } 
\mathrm { x } & \mathrm { f } ( \mathrm { x } ) & \mathrm { g } ( \mathrm { x } ) & \mathrm { h } ( \mathrm { x } ) \
\hline 0 & 1 & 1.5 & 7 \
1 & 2 & 2.25 & 8 \
2 & 4 & 4 & 9 \
3 & 8 & 5 & 10 \
4 & 16 & 7.75 & 11 \
5 & 32 & 12 & 12
\end{array}$$

Accepted Answer

f(x) is exactly expo

Question 11

Find the value of the logarithm without using a calculator.
-log8 32

Accepted Answer

A)  54 
B)  53 
C)  32 
D)  43 
A)  54 
B)  53 
C)  32 
D)  43

Question 12

Graph the function
-$f(x)=\ln x-4$

Accepted Answer

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

Question 13

An earthquake was recorded which was 2,511,886 times more powerful than a reference level zero earthquake. What is the magnitude of this earthquake on the Richter scale? Intensity on the Richter scale is lo $\log \left( \frac { \mathrm { I } } { \mathrm { I } } \right)$

Accepted Answer

A)  5.4 
B)  14.7 
C)  6.4 
D)  0.64 
A)  5.4 
B)  14.7 
C)  6.4 
D)  0.64

Question 14

Graph the function.
-$f ( x ) = e ^ { 3 x } - 3$

Accepted Answer

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

Question 15

Rewrite as a single logarithm.
-$2 \log _ { b } m - \frac { 4 } { 5 } \log _ { b } n + \frac { 1 } { 6 } \log _ { b } j - 4 \log _ { b } k$

Accepted Answer

A)  $\log _ { b } \frac { m ^ { 2 } k ^ { 4 } } { j 1 / 6 n ^ { 4 / 5 } }$ 
B)  $\log _ { b } \frac { m ^ { 2 } n ^ { 4 / 5 } } { j 1 / 6 k ^ { 4 } }$ 
C)  $\log _ { b } \left( 2 m - \frac { 4 } { 5 } n + \frac { 1 } { 6 } j - 4 k \right)$ 
D)  $\log _ { b } \frac { m ^ { 2 } j ^ { 1 / 6 } } { n ^ { 4 / 5 } k ^ { 4 } }$ 
A)  $\log _ { b } \frac { m ^ { 2 } k ^ { 4 } } { j 1 / 6 n ^ { 4 / 5 } }$ 
B)  $\log _ { b } \frac { m ^ { 2 } n ^ { 4 / 5 } } { j 1 / 6 k ^ { 4 } }$ 
C)  $\log _ { b } \left( 2 m - \frac { 4 } { 5 } n + \frac { 1 } { 6 } j - 4 k \right)$ 
D)  $\log _ { b } \frac { m ^ { 2 } j ^ { 1 / 6 } } { n ^ { 4 / 5 } k ^ { 4 } }$

Question 16

Barbara knows that she will need to buy a new car in 2 years. The car will cost $15,000 by then. How much should she invest now at 8%, compounded quarterly, so that she will have enough to buy a new car?

Accepted Answer

A)  $12,802.36 
B)  $13,888.89 
C)  $13,868.34 
D)  $11,907.48 
A)  $12,802.36 
B)  $13,888.89 
C)  $13,868.34 
D)  $11,907.48

Question 17

Evaluate. Round dollar amounts to the nearest cent and other answers to the nearest thousandth when necessary.
-$$1,000 \left( 1 + \frac { \mathrm { r } } { \mathrm { k } } \right) ^ { \mathrm { kn } } \text { for } \mathrm { n } = 7 , \mathrm { r } = 5 \% , \mathrm { k } = 2$$

Accepted Answer

A)  $412.97 
B)  $1412.97 
C)  $1407.10 
D)  $1378.51 
A)  $412.97 
B)  $1412.97 
C)  $1407.10 
D)  $1378.51

Question 18

The number of quarters needed to double an investment when a lump sum is invested at 10%, compounded quarterly, is given b $n = \log 1.025^2$ 2. Use the change of base formula to find n, rounded to the nearest tenth.

Accepted Answer

A)  33.1 quarters 
B)  28.1 quarters 
C)  31.1 quarters 
D)  24.1 quarters 
A)  33.1 quarters 
B)  28.1 quarters 
C)  31.1 quarters 
D)  24.1 quarters

Question 19

In September 1998 the population of the country of West Goma in millions was modeled by $f ( x ) = 17.5 e ^ { 0.0010 x }$. At the same time the population of East Goma in millions was modeled by $\mathrm { g } ( \mathrm { x } ) = 13.7 \mathrm { e } 0.0129 \mathrm { x }$. In both formulas $x$ is the year, where $x = 0$ corresponds to September 1998 . Assuming these trends continue, estimate the year when the population of West Goma will equal the population of East Goma.

Accepted Answer

A)  21 
B)  1977 
C)  2019 
D)  2016 
A)  21 
B)  1977 
C)  2019 
D)  2016

Question 20

Write the logarithmic equation in exponential form.
-$\ln x = - 7$

Accepted Answer

A)  $x = e ^ { 7 }$ 
B)  No solution 
C)  $x = \ln - 7$ 
D)  $x = e ^ { - 7 }$ 
A)  $x = e ^ { 7 }$ 
B)  No solution 
C)  $x = \ln - 7$ 
D)  $x = e ^ { - 7 }$

Graph the function. - $f(x)=3 e^{-x}$ $Graph the function. - f(x)=3 e^{-x}$

Match the equation with its graph. - $y = 2 ^ { - x }$

The number of quarters needed to double an investment when a lump sum is invested at 10%, compounded quarterly, is given b $\mathrm { n } = \frac { \ln 2 } { \ln 1.025 }$ Find n, rounded to the nearest tenth.

Graph the function. - $f(x)=2^{x}$ $Graph the function. - f(x)=2^{x}$

Provide an appropriate response. -If interest is compounded monthly at 5% per year for 14 years, explain how to find the number of compounding periods and the interest rate per compounding period.

The decay of 514 mg of an isotope is given by A( $A ( t ) = 514 e ^ { - 0.021 t }$ , where t is time in years. Find the amount left after 63 years.

Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places. -ln (5 x-2)=ln 12-ln (x-6)

Find the function value. -Let $f ( x ) = \left( \frac { 1 } { 6 } \right) ^ { x }$ . Find $f ( 3 )$ .

Find the inverse of the function. - $f ( x ) = e ^ { - x } + 2$

Find the value of the logarithm without using a calculator. -log8 32

Graph the function - $f(x)=\ln x-4$ $Graph the function - f(x)=\ln x-4$

An earthquake was recorded which was 2,511,886 times more powerful than a reference level zero earthquake. What is the magnitude of this earthquake on the Richter scale? Intensity on the Richter scale is lo $\log \left( \frac { \mathrm { I } } { \mathrm { I } } \right)$

Graph the function. - $f ( x ) = e ^ { 3 x } - 3$ $Graph the function. - f ( x ) = e ^ { 3 x } - 3$

Rewrite as a single logarithm. - $2 \log _ { b } m - \frac { 4 } { 5 } \log _ { b } n + \frac { 1 } { 6 } \log _ { b } j - 4 \log _ { b } k$

Barbara knows that she will need to buy a new car in 2 years. The car will cost $15,000 by then. How much should she invest now at 8%, compounded quarterly, so that she will have enough to buy a new car?

Evaluate. Round dollar amounts to the nearest cent and other answers to the nearest thousandth when necessary. - $1,000 \left( 1 + \frac { \mathrm { r } } { \mathrm { k } } \right) ^ { \mathrm { kn } } \text { for } \mathrm { n } = 7 , \mathrm { r } = 5 \% , \mathrm { k } = 2$

The number of quarters needed to double an investment when a lump sum is invested at 10%, compounded quarterly, is given b $n = \log 1.025^2$ 2. Use the change of base formula to find n, rounded to the nearest tenth.

Write the logarithmic equation in exponential form. - $\ln x = - 7$

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Additional Topics With Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

Exam 5: Exponential and Logarithmic Functions

Graph the function. - f(x)=3e−xf(x)=3 e^{-x}f(x)=3e−x

Match the equation with its graph. - y=2−xy = 2 ^ { - x }y=2−x

The number of quarters needed to double an investment when a lump sum is invested at 10%, compounded quarterly, is given b n=ln⁡2ln⁡1.025\mathrm { n } = \frac { \ln 2 } { \ln 1.025 }n=ln1.025ln2​ Find n, rounded to the nearest tenth.

Graph the function. - f(x)=2xf(x)=2^{x}f(x)=2x

Provide an appropriate response. -If interest is compounded monthly at 5% per year for 14 years, explain how to find the number of compounding periods and the interest rate per compounding period.

The decay of 514 mg of an isotope is given by A( A(t)=514e−0.021tA ( t ) = 514 e ^ { - 0.021 t }A(t)=514e−0.021t , where t is time in years. Find the amount left after 63 years.

Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places. -ln (5 x-2)=ln 12-ln (x-6)

Find the function value. -Let f(x)=(16)xf ( x ) = \left( \frac { 1 } { 6 } \right) ^ { x }f(x)=(61​)x . Find f(3)f ( 3 )f(3) .

Find the inverse of the function. - f(x)=e−x+2f ( x ) = e ^ { - x } + 2f(x)=e−x+2

Find the value of the logarithm without using a calculator. -log8 32

Graph the function - f(x)=ln⁡x−4f(x)=\ln x-4f(x)=lnx−4

An earthquake was recorded which was 2,511,886 times more powerful than a reference level zero earthquake. What is the magnitude of this earthquake on the Richter scale? Intensity on the Richter scale is lo log⁡(II)\log \left( \frac { \mathrm { I } } { \mathrm { I } } \right)log(II​)

Graph the function. - f(x)=e3x−3f ( x ) = e ^ { 3 x } - 3f(x)=e3x−3

Rewrite as a single logarithm. - 2log⁡bm−45log⁡bn+16log⁡bj−4log⁡bk2 \log _ { b } m - \frac { 4 } { 5 } \log _ { b } n + \frac { 1 } { 6 } \log _ { b } j - 4 \log _ { b } k2logb​m−54​logb​n+61​logb​j−4logb​k

Barbara knows that she will need to buy a new car in 2 years. The car will cost $15,000 by then. How much should she invest now at 8%, compounded quarterly, so that she will have enough to buy a new car?

The number of quarters needed to double an investment when a lump sum is invested at 10%, compounded quarterly, is given b n=log⁡1.0252n = \log 1.025^2n=log1.0252 2. Use the change of base formula to find n, rounded to the nearest tenth.

Write the logarithmic equation in exponential form. - ln⁡x=−7\ln x = - 7lnx=−7

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Additional Topics With Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

Graph the function. - $f(x)=3 e^{-x}$ $Graph the function. - f(x)=3 e^{-x}$

Match the equation with its graph. - $y = 2 ^ { - x }$

The number of quarters needed to double an investment when a lump sum is invested at 10%, compounded quarterly, is given b $\mathrm { n } = \frac { \ln 2 } { \ln 1.025 }$ Find n, rounded to the nearest tenth.

Graph the function. - $f(x)=2^{x}$ $Graph the function. - f(x)=2^{x}$

The decay of 514 mg of an isotope is given by A( $A ( t ) = 514 e ^ { - 0.021 t }$ , where t is time in years. Find the amount left after 63 years.

Find the function value. -Let $f ( x ) = \left( \frac { 1 } { 6 } \right) ^ { x }$ . Find $f ( 3 )$ .

Find the inverse of the function. - $f ( x ) = e ^ { - x } + 2$

Graph the function - $f(x)=\ln x-4$ $Graph the function - f(x)=\ln x-4$

An earthquake was recorded which was 2,511,886 times more powerful than a reference level zero earthquake. What is the magnitude of this earthquake on the Richter scale? Intensity on the Richter scale is lo $\log \left( \frac { \mathrm { I } } { \mathrm { I } } \right)$

Graph the function. - $f ( x ) = e ^ { 3 x } - 3$ $Graph the function. - f ( x ) = e ^ { 3 x } - 3$

Rewrite as a single logarithm. - $2 \log _ { b } m - \frac { 4 } { 5 } \log _ { b } n + \frac { 1 } { 6 } \log _ { b } j - 4 \log _ { b } k$

The number of quarters needed to double an investment when a lump sum is invested at 10%, compounded quarterly, is given b $n = \log 1.025^2$ 2. Use the change of base formula to find n, rounded to the nearest tenth.

Write the logarithmic equation in exponential form. - $\ln x = - 7$