Question 1

Find the exponential model that $y = a e ^ { b x }$ fits the points shown in the table. $\begin{array} { | l | l | l | } 
\hline x & 0 & 4 \
\hline y & 15 & 3 \
\hline
\end{array}$

Accepted Answer

A)  $y = 15 e ^ { 05024 x }$ 
B)  $y = \frac { 1 } { 15 } e ^ { - 0.6024 x }$ 
C)  $y = 15 e ^ { - 0.4024 x }$ 
D)  $y = - \frac { 1 } { 15 } e ^ { 0.4024 x }$ 
E)  $y = - \frac { 1 } { 15 } e ^ { - 0.4024 x }$ 
A)  $y = 15 e ^ { 05024 x }$ 
B)  $y = \frac { 1 } { 15 } e ^ { - 0.6024 x }$ 
C)  $y = 15 e ^ { - 0.4024 x }$ 
D)  $y = - \frac { 1 } { 15 } e ^ { 0.4024 x }$ 
E)  $y = - \frac { 1 } { 15 } e ^ { - 0.4024 x }$ C

Question 2

Solve the exponential equation algebraically. Approximate the result to three decimal places. 
$e ^ { 2 x } - 5 e ^ { x } - 6 = 0$

Accepted Answer

A) $\ln 6 \approx 3.792$ 
B)  $\ln 6 \approx 2.792$ 
C)  $\ln 6 \approx 0.792$ 
D)  $\ln 6 \approx - 0.208$ 
E)  $\ln 6 \approx 1.792$ 
A) $\ln 6 \approx 3.792$ 
B)  $\ln 6 \approx 2.792$ 
C)  $\ln 6 \approx 0.792$ 
D)  $\ln 6 \approx - 0.208$ 
E)  $\ln 6 \approx 1.792$ E

Question 3

Condense the expression to the logarithm of a single quantity. $$\log x - 6 \log y + 5 \log z$$

Accepted Answer

A)  $\log \frac { y ^ { 6 } } { x z ^ { 5 } }$ 
B)  $\log \frac { x } { y ^ { 6 } z ^ { 5 } }$ 
C)  $\log \frac { x y ^ { 6 } } { z ^ { 5 } }$ 
D)  $\log \frac { x z ^ { 5 } } { y ^ { 6 } }$ 
E)  $\log \frac { z ^ { 5 } } { x y ^ { 6 } }$ 
A)  $\log \frac { y ^ { 6 } } { x z ^ { 5 } }$ 
B)  $\log \frac { x } { y ^ { 6 } z ^ { 5 } }$ 
C)  $\log \frac { x y ^ { 6 } } { z ^ { 5 } }$ 
D)  $\log \frac { x z ^ { 5 } } { y ^ { 6 } }$ 
E)  $\log \frac { z ^ { 5 } } { x y ^ { 6 } }$ D

Question 4

Evaluate the logarithm using the change-of-base formula. Round your result to three decimal places. $$\log _ { 4 } 6$$

Accepted Answer

A)  $5.292$ 
B)  $1.292$ 
C)  $2.292$ 
D)  $4.292$ 
E)  $3.292$ 
A)  $5.292$ 
B)  $1.292$ 
C)  $2.292$ 
D)  $4.292$ 
E)  $3.292$

Question 5

Determine the principal that must be invested at rate r, compounded monthly, so that $\$ 1,500,000$ will be available for retirement in t years. $r = 5 \% , t = 10$ (Round the answer upto 2 decimal places.)

Accepted Answer

A) $\$ 1,110,741.56$ 
B)  $\$ 1,010,741.56$ 
C)  $\$ 710,741.56$ 
D)  $\$ 810,741.56$ 
E)  $\$ 910,741.56$ 
A) $\$ 1,110,741.56$ 
B)  $\$ 1,010,741.56$ 
C)  $\$ 710,741.56$ 
D)  $\$ 810,741.56$ 
E)  $\$ 910,741.56$

Question 6

Evaluate the logarithm $\log _ { 1 / 3 } 1.877$ using the change of base formula. Round to 3 decimal places.

Accepted Answer

A)  -1.745 
B)  -0.692 
C)  0.630 
D)  0.273 
E)  -0.573 
A)  -1.745 
B)  -0.692 
C)  0.630 
D)  0.273 
E)  -0.573

Question 7

Write the exponential equation in logarithmic form. $$e ^ { 9 x } = 10$$

Accepted Answer

A)  $\ln 10 = - 9 x$ 
B)  $\ln 9 = 10 x$ 
C)  $\ln 10 = 9 x$ 
D) $\ln 10 = \frac { 1 } { 9 } x$ 
E) $\ln 10 = -\frac { 1 } { 9 } x$ 
A)  $\ln 10 = - 9 x$ 
B)  $\ln 9 = 10 x$ 
C)  $\ln 10 = 9 x$ 
D) $\ln 10 = \frac { 1 } { 9 } x$ 
E) $\ln 10 = -\frac { 1 } { 9 } x$

Question 8

Use a graphing utility to construct a table of values for the function. Round your answer to two decimal places. 
$f ( x ) = 6 ^ { - x }$

Accepted Answer

A) 
 $\begin{array}{|c|c|c|c|c|c|}
\hline x & -2 & -1 & 0 & 1 & 2 \
\hline f(x) & 36 & 6 & 1 & 0.17 & -0.03 \
\hline
\end{array}$ 
B) 
$\begin{array}{|c|c|c|c|c|c|}
\hline x & -2 & -1 & 0 & 1 & 2 \
\hline f(x) & -36 & 6 & 1 & 0.17 & 0.03 \
\hline
\end{array}$ 
C) 
$\begin{array}{|c|c|c|c|c|c|}
\hline x & -2 & -1 & 0 & 1 & 2 \
\hline f(x) & 36 & -6 & 1 & 0.17 & 0.03 \
\hline
\end{array}$ 
D) 
$\begin{array}{|c|c|c|c|c|c|}
\hline x & -2 & -1 & 0 & 1 & 2 \
\hline f(x) & 36 & 6 & 1 & -0.17 & 0.03 \
\hline
\end{array}$ 
E) 
$\begin{array}{|c|c|c|c|c|c|}
\hline x & -2 & -1 & 0 & 1 & 2 \
\hline f(x) & 36 & 6 & 1 & 0.17 & 0.03 \
\hline
\end{array}$ 
A) 
 $\begin{array}{|c|c|c|c|c|c|}
\hline x & -2 & -1 & 0 & 1 & 2 \
\hline f(x) & 36 & 6 & 1 & 0.17 & -0.03 \
\hline
\end{array}$ 
B) 
$\begin{array}{|c|c|c|c|c|c|}
\hline x & -2 & -1 & 0 & 1 & 2 \
\hline f(x) & -36 & 6 & 1 & 0.17 & 0.03 \
\hline
\end{array}$ 
C) 
$\begin{array}{|c|c|c|c|c|c|}
\hline x & -2 & -1 & 0 & 1 & 2 \
\hline f(x) & 36 & -6 & 1 & 0.17 & 0.03 \
\hline
\end{array}$ 
D) 
$\begin{array}{|c|c|c|c|c|c|}
\hline x & -2 & -1 & 0 & 1 & 2 \
\hline f(x) & 36 & 6 & 1 & -0.17 & 0.03 \
\hline
\end{array}$ 
E) 
$\begin{array}{|c|c|c|c|c|c|}
\hline x & -2 & -1 & 0 & 1 & 2 \
\hline f(x) & 36 & 6 & 1 & 0.17 & 0.03 \
\hline
\end{array}$

Question 9

Evaluate the function at the indicated value of $x$ . Round your result to three decimal places. 
$ \begin{array}{ll}\text { Function } & \text { Value } \ h(x)=e^{x} & x=7/8\end{array} $

Accepted Answer

A)  $8.07$ 
B)  $0.875$ 
C)  $1.398$ 
D)  $7.5$ 
E)  $0.417$ 
A)  $8.07$ 
B)  $0.875$ 
C)  $1.398$ 
D)  $7.5$ 
E)  $0.417$

Question 10

Find the magnitude R of each earthquake of intensity I (let I0=1). 
$I=230300000$

Accepted Answer

A)  8.36 
B)  9.36 
C)  10.36 
D)  7.36 
E)  6.36 
A)  8.36 
B)  9.36 
C)  10.36 
D)  7.36 
E)  6.36

Question 11

Condense the expression to the logarithm of a single quantity. $$\log x - 2 \log y + 3 \log z$$

Accepted Answer

A) $\log \frac { z ^ { 3 } } { x y ^ { 2 } }$ 
B)  $\log \frac { x } { y ^ { 2 } z ^ { 3 } }$ 
C)  $\log \frac { x y ^ { 2 } } { z ^ { 3 } }$ 
D)  $\log \frac { y ^ { 2 } } { x z ^ { 3 } }$ 
E)  $\log \frac { x z ^ { 3 } } { y ^ { 2 } }$ 
A) $\log \frac { z ^ { 3 } } { x y ^ { 2 } }$ 
B)  $\log \frac { x } { y ^ { 2 } z ^ { 3 } }$ 
C)  $\log \frac { x y ^ { 2 } } { z ^ { 3 } }$ 
D)  $\log \frac { y ^ { 2 } } { x z ^ { 3 } }$ 
E)  $\log \frac { x z ^ { 3 } } { y ^ { 2 } }$

Question 12

Select a scatter plot of the given data.

Accepted Answer

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

Question 13

Evaluate the logarithm $\log _ { 1 / 3 } 1.681$ using the change of base formula. Round to 3 decimal places.

Accepted Answer

A)  -0.473 
B)  0.226 
C)  -0.571 
D)  0.519 
E)  -2.115 
A)  -0.473 
B)  0.226 
C)  -0.571 
D)  0.519 
E)  -2.115

Question 14

Use a graphing utility to construct a table of values for the function. Round your answer to two decimal places. 
$$f ( x ) = 3 ^ { - x }$$

Accepted Answer

A) 
$\begin{array}{|c|c|c|c|c|c|}
\hline x & -2 & -1 & 0 & 1 & 2 \
\hline f(x) & -9 & 3 & 1 & 0.33 & 0.11 \
\hline
\end{array}$ 
B) 
$\begin{array}{|c|c|c|c|c|c|}
\hline x & -2 & -1 & 0 & 1 & 2 \
\hline f(x) & 9 & 3 & 1 & 0.33 & -0.11 \
\hline
\end{array}$ 
C) 
$\begin{array}{|c|c|c|c|c|c|}
\hline x & -2 & -1 & 0 & 1 & 2 \
\hline f(x) & 9 & -3 & 1 & 0.33 & 0.11 \
\hline
\end{array}$ 
D) 
$\begin{array}{|c|c|c|c|c|c|}
\hline x & -2 & -1 & 0 & 1 & 2 \
\hline f(x) & 9 & 3 & 1 & 0.33 & 0.11 \
\hline
\end{array}$ 
E) 
$\begin{array}{|c|c|c|c|c|c|}
\hline x & -2 & -1 & 0 & 1 & 2 \
\hline f(x) & 9 & 3 & 1 & -0.33 & 0.11 \
\hline
\end{array}$ 
A) 
$\begin{array}{|c|c|c|c|c|c|}
\hline x & -2 & -1 & 0 & 1 & 2 \
\hline f(x) & -9 & 3 & 1 & 0.33 & 0.11 \
\hline
\end{array}$ 
B) 
$\begin{array}{|c|c|c|c|c|c|}
\hline x & -2 & -1 & 0 & 1 & 2 \
\hline f(x) & 9 & 3 & 1 & 0.33 & -0.11 \
\hline
\end{array}$ 
C) 
$\begin{array}{|c|c|c|c|c|c|}
\hline x & -2 & -1 & 0 & 1 & 2 \
\hline f(x) & 9 & -3 & 1 & 0.33 & 0.11 \
\hline
\end{array}$ 
D) 
$\begin{array}{|c|c|c|c|c|c|}
\hline x & -2 & -1 & 0 & 1 & 2 \
\hline f(x) & 9 & 3 & 1 & 0.33 & 0.11 \
\hline
\end{array}$ 
E) 
$\begin{array}{|c|c|c|c|c|c|}
\hline x & -2 & -1 & 0 & 1 & 2 \
\hline f(x) & 9 & 3 & 1 & -0.33 & 0.11 \
\hline
\end{array}$

Question 15

Solve the exponential equation algebraically. Approximate the result to three deci- mal places. $$e ^ { 2 x } - 4 e ^ { x } - 5 = 0$$

Accepted Answer

A)  $\ln 5 \approx 3.609$ 
B)  $\ln 5 \approx 0.609$ 
C)  $\ln 5 \approx - 0.391$ 
D)  $\ln 5 \approx 1.609$ 
E)  $\ln 5 \approx 2.609$ 
A)  $\ln 5 \approx 3.609$ 
B)  $\ln 5 \approx 0.609$ 
C)  $\ln 5 \approx - 0.391$ 
D)  $\ln 5 \approx 1.609$ 
E)  $\ln 5 \approx 2.609$

Question 16

Solve for $x$ . Approximate the result to three decimal places. $$\log _ { 3 } x = \frac { 1 } { 2 }$$

Accepted Answer

A)  $\sqrt { 3 } \approx - 1.732$ 
B)  $\frac { \sqrt { 3 } } { 3 } \approx 1.732$ 
C)  $\sqrt { 3 } \approx 1.732$ 
D)  $\sqrt { 3 } = 1.732$ 
E)  $\sqrt { 3 } \approx 2$ 
A)  $\sqrt { 3 } \approx - 1.732$ 
B)  $\frac { \sqrt { 3 } } { 3 } \approx 1.732$ 
C)  $\sqrt { 3 } \approx 1.732$ 
D)  $\sqrt { 3 } = 1.732$ 
E)  $\sqrt { 3 } \approx 2$

Question 17

Determine whether the given x-value is a solution (or an approximate solution) of the equation. $$\begin{array} { l } 
4 ^ { 2 x - 7 } = 64 \
x = 5
\end{array}$$

Accepted Answer

A) True 
 B)False

Question 18

Select a scatter plot of the given data.

Accepted Answer

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

Question 19

Write the exponential equation in logarithmic form. $4 ^ { - 2 } = \frac { 1 } { 16 }$

Accepted Answer

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

Question 20

Determine whether the given x-value is a solution (or an approximate solution) of the equation. 
$\begin{array} { l } 
4 ^ { 5 x - 5 } = 1024 \
x = 2
\end{array}$

Accepted Answer

A) True 
 B)False

Find the exponential model that $y = a e ^ { b x }$ fits the points shown in the table. x 0 4 y 15 3

Solve the exponential equation algebraically. Approximate the result to three decimal places. $e ^ { 2 x } - 5 e ^ { x } - 6 = 0$

Condense the expression to the logarithm of a single quantity. $\log x - 6 \log y + 5 \log z$

Evaluate the logarithm using the change-of-base formula. Round your result to three decimal places. $\log _ { 4 } 6$

Determine the principal that must be invested at rate r, compounded monthly, so that $\$ 1,500,000$ will be available for retirement in t years. $r = 5 \% , t = 10$ (Round the answer upto 2 decimal places.)

Evaluate the logarithm $\log _ { 1 / 3 } 1.877$ using the change of base formula. Round to 3 decimal places.

Write the exponential equation in logarithmic form. $e ^ { 9 x } = 10$

Use a graphing utility to construct a table of values for the function. Round your answer to two decimal places. $f ( x ) = 6 ^ { - x }$

Evaluate the function at the indicated value of $x$ . Round your result to three decimal places. Function Value h(x)= x=7/8

Find the magnitude R of each earthquake of intensity I (let I₀=1). $I=230300000$

Condense the expression to the logarithm of a single quantity. $\log x - 2 \log y + 3 \log z$

Select a scatter plot of the given data.

Evaluate the logarithm $\log _ { 1 / 3 } 1.681$ using the change of base formula. Round to 3 decimal places.

Use a graphing utility to construct a table of values for the function. Round your answer to two decimal places. $f ( x ) = 3 ^ { - x }$

Solve the exponential equation algebraically. Approximate the result to three deci- mal places. $e ^ { 2 x } - 4 e ^ { x } - 5 = 0$

Solve for $x$ . Approximate the result to three decimal places. $\log _ { 3 } x = \frac { 1 } { 2 }$

Determine whether the given x-value is a solution (or an approximate solution) of the equation. =64 x=5

Select a scatter plot of the given data.

Write the exponential equation in logarithmic form. $4 ^ { - 2 } = \frac { 1 } { 16 }$

Determine whether the given x-value is a solution (or an approximate solution) of the equation. =1024 x=2

Functions and Their Graphs

Polynomial and Rational Functions

Trigonometry

Analytic Trigonometry

Topics in Analytic Geometry

Filters

Exam 3: Exponential and Logarithmic Functions

Find the exponential model that y=aebxy = a e ^ { b x }y=aebx fits the points shown in the table. x 0 4 y 15 3

Solve the exponential equation algebraically. Approximate the result to three decimal places. e2x−5ex−6=0e ^ { 2 x } - 5 e ^ { x } - 6 = 0e2x−5ex−6=0

Condense the expression to the logarithm of a single quantity. log⁡x−6log⁡y+5log⁡z\log x - 6 \log y + 5 \log zlogx−6logy+5logz

Evaluate the logarithm using the change-of-base formula. Round your result to three decimal places. log⁡46\log _ { 4 } 6log4​6

Determine the principal that must be invested at rate r, compounded monthly, so that $1,500,000\$ 1,500,000$1,500,000 will be available for retirement in t years. r=5%,t=10r = 5 \% , t = 10r=5%,t=10 (Round the answer upto 2 decimal places.)

Evaluate the logarithm log⁡1/31.877\log _ { 1 / 3 } 1.877log1/3​1.877 using the change of base formula. Round to 3 decimal places.

Write the exponential equation in logarithmic form. e9x=10e ^ { 9 x } = 10e9x=10

Use a graphing utility to construct a table of values for the function. Round your answer to two decimal places. f(x)=6−xf ( x ) = 6 ^ { - x }f(x)=6−x

Evaluate the function at the indicated value of xxx . Round your result to three decimal places. Function Value h(x)= x=7/8

Find the magnitude R of each earthquake of intensity I (let I0=1). I=230300000I=230300000I=230300000

Condense the expression to the logarithm of a single quantity. log⁡x−2log⁡y+3log⁡z\log x - 2 \log y + 3 \log zlogx−2logy+3logz

Select a scatter plot of the given data.

Evaluate the logarithm log⁡1/31.681\log _ { 1 / 3 } 1.681log1/3​1.681 using the change of base formula. Round to 3 decimal places.

Use a graphing utility to construct a table of values for the function. Round your answer to two decimal places. f(x)=3−xf ( x ) = 3 ^ { - x }f(x)=3−x

Solve the exponential equation algebraically. Approximate the result to three deci- mal places. e2x−4ex−5=0e ^ { 2 x } - 4 e ^ { x } - 5 = 0e2x−4ex−5=0

Solve for xxx . Approximate the result to three decimal places. log⁡3x=12\log _ { 3 } x = \frac { 1 } { 2 }log3​x=21​

Determine whether the given x-value is a solution (or an approximate solution) of the equation. =64 x=5

Select a scatter plot of the given data.

Write the exponential equation in logarithmic form. 4−2=1164 ^ { - 2 } = \frac { 1 } { 16 }4−2=161​

Determine whether the given x-value is a solution (or an approximate solution) of the equation. =1024 x=2

Functions and Their Graphs

Polynomial and Rational Functions

Trigonometry

Analytic Trigonometry

Topics in Analytic Geometry

Filters

Find the exponential model that $y = a e ^ { b x }$ fits the points shown in the table. x 0 4 y 15 3

Solve the exponential equation algebraically. Approximate the result to three decimal places. $e ^ { 2 x } - 5 e ^ { x } - 6 = 0$

Condense the expression to the logarithm of a single quantity. $\log x - 6 \log y + 5 \log z$

Evaluate the logarithm using the change-of-base formula. Round your result to three decimal places. $\log _ { 4 } 6$

Determine the principal that must be invested at rate r, compounded monthly, so that $\$ 1,500,000$ will be available for retirement in t years. $r = 5 \% , t = 10$ (Round the answer upto 2 decimal places.)

Evaluate the logarithm $\log _ { 1 / 3 } 1.877$ using the change of base formula. Round to 3 decimal places.

Write the exponential equation in logarithmic form. $e ^ { 9 x } = 10$

Use a graphing utility to construct a table of values for the function. Round your answer to two decimal places. $f ( x ) = 6 ^ { - x }$

Evaluate the function at the indicated value of $x$ . Round your result to three decimal places. Function Value h(x)= x=7/8

Find the magnitude R of each earthquake of intensity I (let I₀=1). $I=230300000$

Condense the expression to the logarithm of a single quantity. $\log x - 2 \log y + 3 \log z$

Evaluate the logarithm $\log _ { 1 / 3 } 1.681$ using the change of base formula. Round to 3 decimal places.

Use a graphing utility to construct a table of values for the function. Round your answer to two decimal places. $f ( x ) = 3 ^ { - x }$

Solve the exponential equation algebraically. Approximate the result to three deci- mal places. $e ^ { 2 x } - 4 e ^ { x } - 5 = 0$

Solve for $x$ . Approximate the result to three decimal places. $\log _ { 3 } x = \frac { 1 } { 2 }$

Write the exponential equation in logarithmic form. $4 ^ { - 2 } = \frac { 1 } { 16 }$