Question 1

Solve the exponential equation below algebraically. Round your result to three decimal places. $150 e ^ { - 0.01 x } = 140,000$

Accepted Answer

A)  -704.498 
B)  -695.069 
C)  -682.289 
D)  -683.876 
E)  -707.153 
A)  -704.498 
B)  -695.069 
C)  -682.289 
D)  -683.876 
E)  -707.153 D

Question 2

Find the exact value of $\ln e ^ { 1.50 } - \ln \sqrt { e }$ without using a calculator.

Accepted Answer

A)  0.75 
B)  3 
C)  1 
D)  2 
E)  1.5 
A)  0.75 
B)  3 
C)  1 
D)  2 
E)  1.5 C

Question 3

Evaluate the function $f ( x ) = \log _ { 2 } x$ at $x = \frac { 1 } { 2 }$ without using a calculator.

Accepted Answer

A)  $0$ 
B)  $- 1$ 
C)  $- 2$ 
D)  $2$ 
E)  $\frac { 1 } { 2 }$ 
A)  $0$ 
B)  $- 1$ 
C)  $- 2$ 
D)  $2$ 
E)  $\frac { 1 } { 2 }$ B

Question 4

Find the exponential model $y = a e ^ { b x }$ that fits the points shown in the table below. Round parameters to the nearest thousandth.
$\begin{array}{|c|c|c|}
\hline x & 0 & 1 \
\hline y & 5 & 10 \
\hline
\end{array}$

Accepted Answer

A)  $y = 5 e ^ { 0.693 x }$ 
B)  $y = 0.693 e ^ { - 5 x }$ 
C)  $y = - 5 e ^ { - 0.693 x }$ 
D)  $y = 5 e ^ { - 0.693 x }$ 
E)  $y = 0.693 e ^ { 5 x }$ 
A)  $y = 5 e ^ { 0.693 x }$ 
B)  $y = 0.693 e ^ { - 5 x }$ 
C)  $y = - 5 e ^ { - 0.693 x }$ 
D)  $y = 5 e ^ { - 0.693 x }$ 
E)  $y = 0.693 e ^ { 5 x }$

Question 5

Determine whether or not $x = \frac { 4 } { 7 } \text { is a solution to } 3 ^ { 4 x - 3 } = 81$

Accepted Answer

A) True 
 B)False

Question 6

Solve the logarithmic equation below algebraically. Round your result to three decimal places. $\ln \left( x ^ { 2 } + 6 \right) = 5$

Accepted Answer

A)  $\pm 11.604$ 
B)  $\pm 14.688$ 
C)  $\pm 15.639$ 
D)  $\pm 12.762$ 
E)  $\pm 11.934$ 
A)  $\pm 11.604$ 
B)  $\pm 14.688$ 
C)  $\pm 15.639$ 
D)  $\pm 12.762$ 
E)  $\pm 11.934$

Question 7

Determine whether or not $x = \frac { 4 } { 7 } \text { is a solution to } 3 ^ { 4 x - 3 } = 81 \text {. }$

Accepted Answer

A) True 
 B)False

Question 8

Match the function $y = \frac { 3 } { 1 + e ^ { - 2 x } }$ with its graph.
Graph I:

Graph II:

Graph III:
 
 Graph IV:

Graph V:

Accepted Answer

A)  Graph V 
B)  Graph II 
C)  Graph I 
D)  Graph III 
E)  Graph IV 
A)  Graph V 
B)  Graph II 
C)  Graph I 
D)  Graph III 
E)  Graph IV

Question 9

Solve for $x : e ^ { x } \left( 8 - e ^ { x } \right) = 16$ . Round to 3 decimal places.

Accepted Answer

A)  3.079 
B)  2.079 
C)  1.386 
D)  2980.958 
E)  no solution 
A)  3.079 
B)  2.079 
C)  1.386 
D)  2980.958 
E)  no solution

Question 10

Find the exact value of $\ln e ^ { 2.50 } - \ln \sqrt { e }$ without using a calculator.

Accepted Answer

A)  1.25 
B)  5 
C)  2 
D)  3 
E)  2.5 
A)  1.25 
B)  5 
C)  2 
D)  3 
E)  2.5

Question 11

Determine whether the scatter plot below could best be modeled by a linear model, a quadratic model, an exponential model, a logarithmic model, or a logistic model.

Accepted Answer

A)  a logistic model 
B)  an exponential model 
C)  a linear model 
D)  a logarithmic model 
E)  a quadratic model 
A)  a logistic model 
B)  an exponential model 
C)  a linear model 
D)  a logarithmic model 
E)  a quadratic model

Question 12

Determine whether the scatter plot below could best be modeled by a linear model, a quadratic model, an exponential model, a logarithmic model, or a logistic model.

Accepted Answer

A)  a linear model 
B)  a quadratic model 
C)  a logistic model 
D)  an exponential model 
E)  a logarithmic model 
A)  a linear model 
B)  a quadratic model 
C)  a logistic model 
D)  an exponential model 
E)  a logarithmic model

Question 13

A sample contains 60 grams of carbon $\left( { } ^ { 14 } C \right) . { } ^ { 14 } C$ has a half-life of 5715 years. How much ${ } ^ { 14 } C$ remains after 1900 years? Round your answer to three decimal places.

Accepted Answer

A)  $40.052$ grams 
B)  $47.651$ grams 
C)  $33.913$ grams 
D)  $19.948$ grams 
E)  $32.913$ grams 
A)  $40.052$ grams 
B)  $47.651$ grams 
C)  $33.913$ grams 
D)  $19.948$ grams 
E)  $32.913$ grams

Question 14

Evaluate the function $f ( x ) = \log _ { 4 } x$ at $x = \frac { 1 } { 64 }$ without using a calculator.

Accepted Answer

A)  $- 2$ 
B)  $- 3$ 
C)  $- 4$ 
D)  64 
E)  $\frac { 1 } { 64 }$ 
A)  $- 2$ 
B)  $- 3$ 
C)  $- 4$ 
D)  64 
E)  $\frac { 1 } { 64 }$

Question 15

Rewrite the logarithm $\log _ { 4 } 25$ in terms of the natural logarithm.

Accepted Answer

A)  $\frac { \ln 25 } { \ln 4 }$ 
B)  $\frac { \ln 4 } { \ln 25 }$ 
C)  $\ln 4 \ln 25$ 
D)  $\frac { \ln 25 } { \log _ { 4 } e }$ 
E)  $\ln 25$ 
A)  $\frac { \ln 25 } { \ln 4 }$ 
B)  $\frac { \ln 4 } { \ln 25 }$ 
C)  $\ln 4 \ln 25$ 
D)  $\frac { \ln 25 } { \log _ { 4 } e }$ 
E)  $\ln 25$

Question 16

Match the function $y = 2 e ^ { - x }$ with its graph.
Graph I:

Graph II:

Graph III:

Graph IV:
  Graph V:

Accepted Answer

A)  Graph III 
B)  Graph V 
C)  Graph IV 
D)  Graph I 
E)  Graph II 
A)  Graph III 
B)  Graph V 
C)  Graph IV 
D)  Graph I 
E)  Graph II

Question 17

Rewrite the logarithmic equation $\log _ { 4 } \frac { 1 } { 16 } = - 2$ in exponential form.

Accepted Answer

A)  $4 ^ { 16 } = - 2$ 
B)  $4 ^ { 1 / 16 } = - 2$ 
C)  $4 ^ { - 2 } = \frac { 1 } { 16 }$ 
D)  $\left( \frac { 1 } { 16 } \right) ^ { - 2 } = 4$ 
E)  $4 ^ { - 2 } = - \frac { 1 } { 16 }$ 
A)  $4 ^ { 16 } = - 2$ 
B)  $4 ^ { 1 / 16 } = - 2$ 
C)  $4 ^ { - 2 } = \frac { 1 } { 16 }$ 
D)  $\left( \frac { 1 } { 16 } \right) ^ { - 2 } = 4$ 
E)  $4 ^ { - 2 } = - \frac { 1 } { 16 }$

Question 18

Solve the equation below algebraically. Round your result to three decimal places.
$e ^ { x } + 4 x e ^ { x } = 0$

Accepted Answer

A)  $- 0.367$ 
B)  $- 0.001$ 
C)  $- 1.036$ 
D)  $- 0.136$ 
E)  $- 0.250$ 
A)  $- 0.367$ 
B)  $- 0.001$ 
C)  $- 1.036$ 
D)  $- 0.136$ 
E)  $- 0.250$

Question 19

Solve the exponential equation below algebraically. Round your result to three decimal places. 
$e ^ { 2 x } + 3 e ^ { x } - 18 = 0$

Accepted Answer

A)  $1.099$ 
B)  $0.214$ 
C)  $2.077$ 
D)  $- 0.188$ 
E)  $3.271$ 
A)  $1.099$ 
B)  $0.214$ 
C)  $2.077$ 
D)  $- 0.188$ 
E)  $3.271$

Question 20

Find the exact value of $\log _ { 4 } 12 - \log _ { 4 } 3$ without using a calculator.

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  1 
C)  3 
D)  $\frac { 3 } { 2 }$ 
E)  4 
A)  $\frac { 1 } { 2 }$ 
B)  1 
C)  3 
D)  $\frac { 3 } { 2 }$ 
E)  4

Solve the exponential equation below algebraically. Round your result to three decimal places. $150 e ^ { - 0.01 x } = 140,000$

Find the exact value of $\ln e ^ { 1.50 } - \ln \sqrt { e }$ without using a calculator.

Evaluate the function $f ( x ) = \log _ { 2 } x$ at $x = \frac { 1 } { 2 }$ without using a calculator.

Find the exponential model $y = a e ^ { b x }$ that fits the points shown in the table below. Round parameters to the nearest thousandth. x 0 1 y 5 10

Determine whether or not $x = \frac { 4 } { 7 } \text { is a solution to } 3 ^ { 4 x - 3 } = 81$

Solve the logarithmic equation below algebraically. Round your result to three decimal places. $\ln \left( x ^ { 2 } + 6 \right) = 5$

Determine whether or not $x = \frac { 4 } { 7 } \text { is a solution to } 3 ^ { 4 x - 3 } = 81 \text {. }$

Solve for $x : e ^ { x } \left( 8 - e ^ { x } \right) = 16$ . Round to 3 decimal places.

Find the exact value of $\ln e ^ { 2.50 } - \ln \sqrt { e }$ without using a calculator.

Determine whether the scatter plot below could best be modeled by a linear model, a quadratic model, an exponential model, a logarithmic model, or a logistic model.

Determine whether the scatter plot below could best be modeled by a linear model, a quadratic model, an exponential model, a logarithmic model, or a logistic model.

A sample contains 60 grams of carbon $\left( { } ^ { 14 } C \right) . { } ^ { 14 } C$ has a half-life of 5715 years. How much ${ } ^ { 14 } C$ remains after 1900 years? Round your answer to three decimal places.

Evaluate the function $f ( x ) = \log _ { 4 } x$ at $x = \frac { 1 } { 64 }$ without using a calculator.

Rewrite the logarithm $\log _ { 4 } 25$ in terms of the natural logarithm.

Rewrite the logarithmic equation $\log _ { 4 } \frac { 1 } { 16 } = - 2$ in exponential form.

Solve the equation below algebraically. Round your result to three decimal places. $e ^ { x } + 4 x e ^ { x } = 0$

Solve the exponential equation below algebraically. Round your result to three decimal places. $e ^ { 2 x } + 3 e ^ { x } - 18 = 0$

Find the exact value of $\log _ { 4 } 12 - \log _ { 4 } 3$ without using a calculator.

Functions and Their Graphs

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Review of Graphs, Equations, and Inequalities

Filters

Exam 3: Exponential and Logarithmic Functions

Solve the exponential equation below algebraically. Round your result to three decimal places. 150e−0.01x=140,000150 e ^ { - 0.01 x } = 140,000150e−0.01x=140,000

Find the exact value of ln⁡e1.50−ln⁡e\ln e ^ { 1.50 } - \ln \sqrt { e }lne1.50−lne​ without using a calculator.

Evaluate the function f(x)=log⁡2xf ( x ) = \log _ { 2 } xf(x)=log2​x at x=12x = \frac { 1 } { 2 }x=21​ without using a calculator.

Find the exponential model y=aebxy = a e ^ { b x }y=aebx that fits the points shown in the table below. Round parameters to the nearest thousandth. x 0 1 y 5 10

Determine whether or not x=47 is a solution to 34x−3=81x = \frac { 4 } { 7 } \text { is a solution to } 3 ^ { 4 x - 3 } = 81x=74​ is a solution to 34x−3=81

Solve the logarithmic equation below algebraically. Round your result to three decimal places. ln⁡(x2+6)=5\ln \left( x ^ { 2 } + 6 \right) = 5ln(x2+6)=5

Determine whether or not x=47 is a solution to 34x−3=81. x = \frac { 4 } { 7 } \text { is a solution to } 3 ^ { 4 x - 3 } = 81 \text {. }x=74​ is a solution to 34x−3=81.

Match the function y=31+e−2xy = \frac { 3 } { 1 + e ^ { - 2 x } }y=1+e−2x3​ with its graph. Graph I: Graph II: Graph III: Graph IV: Graph V:

Solve for x:ex(8−ex)=16x : e ^ { x } \left( 8 - e ^ { x } \right) = 16x:ex(8−ex)=16 . Round to 3 decimal places.

Find the exact value of ln⁡e2.50−ln⁡e\ln e ^ { 2.50 } - \ln \sqrt { e }lne2.50−lne​ without using a calculator.

Determine whether the scatter plot below could best be modeled by a linear model, a quadratic model, an exponential model, a logarithmic model, or a logistic model.

Determine whether the scatter plot below could best be modeled by a linear model, a quadratic model, an exponential model, a logarithmic model, or a logistic model.

A sample contains 60 grams of carbon (14C).14C\left( { } ^ { 14 } C \right) . { } ^ { 14 } C(14C).14C has a half-life of 5715 years. How much 14C{ } ^ { 14 } C14C remains after 1900 years? Round your answer to three decimal places.

Evaluate the function f(x)=log⁡4xf ( x ) = \log _ { 4 } xf(x)=log4​x at x=164x = \frac { 1 } { 64 }x=641​ without using a calculator.

Rewrite the logarithm log⁡425\log _ { 4 } 25log4​25 in terms of the natural logarithm.

Match the function y=2e−xy = 2 e ^ { - x }y=2e−x with its graph. Graph I: Graph II: Graph III: Graph IV: Graph V:

Rewrite the logarithmic equation log⁡4116=−2\log _ { 4 } \frac { 1 } { 16 } = - 2log4​161​=−2 in exponential form.

Solve the equation below algebraically. Round your result to three decimal places. ex+4xex=0e ^ { x } + 4 x e ^ { x } = 0ex+4xex=0

Solve the exponential equation below algebraically. Round your result to three decimal places. e2x+3ex−18=0e ^ { 2 x } + 3 e ^ { x } - 18 = 0e2x+3ex−18=0

Find the exact value of log⁡412−log⁡43\log _ { 4 } 12 - \log _ { 4 } 3log4​12−log4​3 without using a calculator.

Functions and Their Graphs

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Review of Graphs, Equations, and Inequalities

Filters

Solve the exponential equation below algebraically. Round your result to three decimal places. $150 e ^ { - 0.01 x } = 140,000$

Find the exact value of $\ln e ^ { 1.50 } - \ln \sqrt { e }$ without using a calculator.

Evaluate the function $f ( x ) = \log _ { 2 } x$ at $x = \frac { 1 } { 2 }$ without using a calculator.

Find the exponential model $y = a e ^ { b x }$ that fits the points shown in the table below. Round parameters to the nearest thousandth. x 0 1 y 5 10

Determine whether or not $x = \frac { 4 } { 7 } \text { is a solution to } 3 ^ { 4 x - 3 } = 81$

Solve the logarithmic equation below algebraically. Round your result to three decimal places. $\ln \left( x ^ { 2 } + 6 \right) = 5$

Determine whether or not $x = \frac { 4 } { 7 } \text { is a solution to } 3 ^ { 4 x - 3 } = 81 \text {. }$

Solve for $x : e ^ { x } \left( 8 - e ^ { x } \right) = 16$ . Round to 3 decimal places.

Find the exact value of $\ln e ^ { 2.50 } - \ln \sqrt { e }$ without using a calculator.

A sample contains 60 grams of carbon $\left( { } ^ { 14 } C \right) . { } ^ { 14 } C$ has a half-life of 5715 years. How much ${ } ^ { 14 } C$ remains after 1900 years? Round your answer to three decimal places.

Evaluate the function $f ( x ) = \log _ { 4 } x$ at $x = \frac { 1 } { 64 }$ without using a calculator.

Rewrite the logarithm $\log _ { 4 } 25$ in terms of the natural logarithm.

Rewrite the logarithmic equation $\log _ { 4 } \frac { 1 } { 16 } = - 2$ in exponential form.

Solve the equation below algebraically. Round your result to three decimal places. $e ^ { x } + 4 x e ^ { x } = 0$

Solve the exponential equation below algebraically. Round your result to three decimal places. $e ^ { 2 x } + 3 e ^ { x } - 18 = 0$

Find the exact value of $\log _ { 4 } 12 - \log _ { 4 } 3$ without using a calculator.