Question 1

Use a graphing utility to construct a table of values for the function.Round your answer to two decimal places.​ $f ( x ) = 2 ^ { x - 1 } + 2$ ​

Accepted Answer

A)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 2.13 & 2.25 & 2.50 & 3.00 & 4.00 \
\hline
\end{array}$$ 
B)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 2.13 & 2.25 & - 2.50 & 3.00 & 4.00 \
\hline
\end{array}$$ 
C)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 2.13 & - 2.25 & 2.50 & 3.00 & 4.00 \
\hline
\end{array}$$ 
D)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 2.13 & 2.25 & 2.50 & - 3.00 & - 4.00 \
\hline
\end{array}$$ 
E)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & - 2.13 & 2.25 & 2.50 & 3.00 & 4.00 \
\hline
\end{array}$$ 
A)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 2.13 & 2.25 & 2.50 & 3.00 & 4.00 \
\hline
\end{array}$$ 
B)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 2.13 & 2.25 & - 2.50 & 3.00 & 4.00 \
\hline
\end{array}$$ 
C)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 2.13 & - 2.25 & 2.50 & 3.00 & 4.00 \
\hline
\end{array}$$ 
D)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 2.13 & 2.25 & 2.50 & - 3.00 & - 4.00 \
\hline
\end{array}$$ 
E)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & - 2.13 & 2.25 & 2.50 & 3.00 & 4.00 \
\hline
\end{array}$$

Question 2

Select the graph of the exponential function.​ $$y = 1.02 ^ { - 2 x }$$ ​

Accepted Answer

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

Question 3

Evaluate the function $f ( x ) = 400 ( 1.005 ) ^ { x }$ at $x = 240$ .Round to 3 decimal places.

Accepted Answer

A) 1,324.082 
B) 1,764.558 
C) 404.010 
D) 96,480.000 
E) 3.310 
A) 1,324.082 
B) 1,764.558 
C) 404.010 
D) 96,480.000 
E) 3.310

Question 4

Match the graph with its exponential function.​   ​

Accepted Answer

A)  $$y = 4 ^ { x }$$ 
B)  $y = - 4 ^ { - x }$ 
C)  $y = - 4 ^ { x }$ 
D)  $y = 4 ^ { - x }$ 
E)  $y = 4 x$ 
A)  $$y = 4 ^ { x }$$ 
B)  $y = - 4 ^ { - x }$ 
C)  $y = - 4 ^ { x }$ 
D)  $y = 4 ^ { - x }$ 
E)  $y = 4 x$

Question 5

Graph the exponential function.​ $f ( x ) = 4 ^ { x } + 1$ ​

Accepted Answer

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

Question 6

Find the value of b that would cause the graph of y = bx to look like the graph indicated.​   ​

Accepted Answer

A)  $$b = \frac { 1 } { 4 }$$ 
B)  $b = \frac { 3 } { 4 }$ 
C)  $b = 4$ 
D)  $$b = - 4$$ 
E)  $b = - \frac { 1 } { 4 }$ 
A)  $$b = \frac { 1 } { 4 }$$ 
B)  $b = \frac { 3 } { 4 }$ 
C)  $b = 4$ 
D)  $$b = - 4$$ 
E)  $b = - \frac { 1 } { 4 }$

Question 7

Use the One-to-One Property to solve the equation for x.​ $e ^ { x ^ { 2 } - 4 } = e ^ { 3 x }$ ​

Accepted Answer

A)  $x = - 4$ 
B)  $x = 3$ 
C)  $x = 4 , - 1$ 
D)  $x = - 4 , - 1$ 
E)  $x = - 4,1$ 
A)  $x = - 4$ 
B)  $x = 3$ 
C)  $x = 4 , - 1$ 
D)  $x = - 4 , - 1$ 
E)  $x = - 4,1$

Question 8

Select the graph of the exponential function.​ $$f ( x ) = 6 ^ { x - 2 } + 6$$ ​

Accepted Answer

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

Question 9

What is the value of the function $$f ( x ) = 4.8 e ^ { - 1.7 x }$$ at $x = 2.5$ ? Round to 3 decimal places.

Accepted Answer

A) 10.683 
B) 0.000 
C) -55.453 
D) 0.877 
E) 0.068 
A) 10.683 
B) 0.000 
C) -55.453 
D) 0.877 
E) 0.068

Question 10

Evaluate the function $f ( x ) = 1.3 ^ { x }$ at $x = 2.7$ .Round to 3 decimal places.

Accepted Answer

A) 1.690 
B) 2.031 
C) 3.637 
D) 9.477 
E) 3.510 
A) 1.690 
B) 2.031 
C) 3.637 
D) 9.477 
E) 3.510

Question 11

Use the One-to-One Property to solve the following equation for x.​ $\left( \frac { 1 } { 3 } \right) ^ { 8 x - 1 } = 27$ ​

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $- \frac { 1 } { 4 }$ 
C)  $\frac { 1 } { 3 }$ 
D)  $- \frac { 3 } { 8 }$ 
E)  $\frac { 1 } { 8 }$ 
A)  $\frac { 1 } { 2 }$ 
B)  $- \frac { 1 } { 4 }$ 
C)  $\frac { 1 } { 3 }$ 
D)  $- \frac { 3 } { 8 }$ 
E)  $\frac { 1 } { 8 }$

Question 12

Graph the function using translations.​ $f ( x ) = 3 ^ { x + 1 }$ ​

Accepted Answer

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

Question 13

Select the graph of the exponential function.​ $$s ( t ) = 3 e ^ { 0.13 t }$$ ​

Accepted Answer

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

Question 14

Select the graph of the function.​ $$f ( x ) = 6 e ^ { x - 2 } + 7$$ ​

Accepted Answer

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

Question 15

What is the value of the function $f ( x ) = 125 e ^ { 0.8 x }$ at $x = 2.3$ ? Round to 3 decimal places.

Accepted Answer

A) 278.193 
B) 127.226 
C) 74.820 
D) 787.067 
E) 8647.887 
A) 278.193 
B) 127.226 
C) 74.820 
D) 787.067 
E) 8647.887

Question 16

Use a graphing utility to determine which graph below is the graph of the function. ​​ $g ( x ) = 0.1 e ^ { - 4 x }$ ​

Accepted Answer

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

Question 17

Use the One-to-One Property to solve the following equation for x. $$2 ^ { 3 x } = 128$$ ​

Accepted Answer

A)  $$\frac { 7 } { 3 }$$ 
B)  $$\frac { 3 } { 7 }$$ 
C)  $\frac { 128 } { 3 }$ 
D) 2 
E)  $- \frac { 64 } { 3 }$ 
A)  $$\frac { 7 } { 3 }$$ 
B)  $$\frac { 3 } { 7 }$$ 
C)  $\frac { 128 } { 3 }$ 
D) 2 
E)  $- \frac { 64 } { 3 }$

Question 18

Let Q represent a mass of radioactive radium (226Ra)(in grams),whose half-life is 1599 years.The quantity of radium present after t years is $Q = 5 \left( \frac { 1 } { 2 } \right) ^ { t / 1599 }$ Determine the quantity present after 300 years.Round to the nearest hundredth of a gram.

Accepted Answer

A) 0 g 
B) 0.47 g 
C) 5.00 g 
D) 4.39 g 
E) 0.88 g 
A) 0 g 
B) 0.47 g 
C) 5.00 g 
D) 4.39 g 
E) 0.88 g

Question 19

Use properties of exponents to determine which functions (if any)are the same.​ $\begin{array} { l } 
f ( x ) = 6 ^ { x - 2 } \
g ( x ) = 6 ^ { x } - 36 \
f ( x ) = \frac { 1 } { 36 } \left( 6 ^ { x } \right)
\end{array}$ ​

Accepted Answer

A)  $f ( x ) = h ( x )$ 
B)  $f ( x ) = - g ( x )$ 
C)  $f ( x ) = g ( x )$ 
D)  $g ( x ) = h ( x )$ 
E)  $g ( x ) = - h ( x )$ 
A)  $f ( x ) = h ( x )$ 
B)  $f ( x ) = - g ( x )$ 
C)  $f ( x ) = g ( x )$ 
D)  $g ( x ) = h ( x )$ 
E)  $g ( x ) = - h ( x )$

Exam 18: Exponential Functions and Their Graphs

Use a graphing utility to construct a table of values for the function.Round your answer to two decimal places.​ f(x)=2x−1+2f ( x ) = 2 ^ { x - 1 } + 2f(x)=2x−1+2 ​

Select the graph of the exponential function.​ y=1.02−2xy = 1.02 ^ { - 2 x }y=1.02−2x ​

Evaluate the function f(x)=400(1.005)xf ( x ) = 400 ( 1.005 ) ^ { x }f(x)=400(1.005)x at x=240x = 240x=240 .Round to 3 decimal places.

Match the graph with its exponential function.​ ​

Graph the exponential function.​ f(x)=4x+1f ( x ) = 4 ^ { x } + 1f(x)=4x+1 ​

Find the value of b that would cause the graph of y = bx to look like the graph indicated.​ ​

Use the One-to-One Property to solve the equation for x.​ ex2−4=e3xe ^ { x ^ { 2 } - 4 } = e ^ { 3 x }ex2−4=e3x ​

Select the graph of the exponential function.​ f(x)=6x−2+6f ( x ) = 6 ^ { x - 2 } + 6f(x)=6x−2+6 ​

What is the value of the function f(x)=4.8e−1.7xf ( x ) = 4.8 e ^ { - 1.7 x }f(x)=4.8e−1.7x at x=2.5x = 2.5x=2.5 ? Round to 3 decimal places.

Evaluate the function f(x)=1.3xf ( x ) = 1.3 ^ { x }f(x)=1.3x at x=2.7x = 2.7x=2.7 .Round to 3 decimal places.

Use the One-to-One Property to solve the following equation for x.​ (13)8x−1=27\left( \frac { 1 } { 3 } \right) ^ { 8 x - 1 } = 27(31​)8x−1=27 ​

Graph the function using translations.​ f(x)=3x+1f ( x ) = 3 ^ { x + 1 }f(x)=3x+1 ​

Select the graph of the exponential function.​ s(t)=3e0.13ts ( t ) = 3 e ^ { 0.13 t }s(t)=3e0.13t ​

Select the graph of the function.​ f(x)=6ex−2+7f ( x ) = 6 e ^ { x - 2 } + 7f(x)=6ex−2+7 ​

What is the value of the function f(x)=125e0.8xf ( x ) = 125 e ^ { 0.8 x }f(x)=125e0.8x at x=2.3x = 2.3x=2.3 ? Round to 3 decimal places.

Use a graphing utility to determine which graph below is the graph of the function. ​​ g(x)=0.1e−4xg ( x ) = 0.1 e ^ { - 4 x }g(x)=0.1e−4x ​

Use the One-to-One Property to solve the following equation for x. 23x=1282 ^ { 3 x } = 12823x=128 ​

Use properties of exponents to determine which functions (if any)are the same.​ f(x)= g(x)=-36 f(x)= ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Use a graphing utility to construct a table of values for the function.Round your answer to two decimal places. $f ( x ) = 2 ^ { x - 1 } + 2$

Select the graph of the exponential function. $y = 1.02 ^ { - 2 x }$

Evaluate the function $f ( x ) = 400 ( 1.005 ) ^ { x }$ at $x = 240$ .Round to 3 decimal places.

Match the graph with its exponential function.

Graph the exponential function. $f ( x ) = 4 ^ { x } + 1$

Find the value of b that would cause the graph of y = b^x to look like the graph indicated.

Use the One-to-One Property to solve the equation for x. $e ^ { x ^ { 2 } - 4 } = e ^ { 3 x }$

Select the graph of the exponential function. $f ( x ) = 6 ^ { x - 2 } + 6$

What is the value of the function $f ( x ) = 4.8 e ^ { - 1.7 x }$ at $x = 2.5$ ? Round to 3 decimal places.

Evaluate the function $f ( x ) = 1.3 ^ { x }$ at $x = 2.7$ .Round to 3 decimal places.

Use the One-to-One Property to solve the following equation for x. $\left( \frac { 1 } { 3 } \right) ^ { 8 x - 1 } = 27$

Graph the function using translations. $f ( x ) = 3 ^ { x + 1 }$

Select the graph of the exponential function. $s ( t ) = 3 e ^ { 0.13 t }$

Select the graph of the function. $f ( x ) = 6 e ^ { x - 2 } + 7$

What is the value of the function $f ( x ) = 125 e ^ { 0.8 x }$ at $x = 2.3$ ? Round to 3 decimal places.

Use a graphing utility to determine which graph below is the graph of the function. $g ( x ) = 0.1 e ^ { - 4 x }$

Use the One-to-One Property to solve the following equation for x. $2 ^ { 3 x } = 128$

Use properties of exponents to determine which functions (if any)are the same. f(x)= g(x)=-36 f(x)=