Deck 18: Exponential Functions and Their Graphs

Question 1

Match the graph with its exponential function.​ ​

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

Answer 1

$$y = 4 ^ { x }$$

Question 2

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

A)​ ​
B)​
C)​
D)​
E)​

Answer 2

​

Question 3

Evaluate the function at the indicated value of x.Round the result to three decimal places. ​
Function
Value $h ( x ) = 4000 e ^ { 0.06 x }$ $x = 5$

A) $5599.435$
B) $5499.435$
C) $5449.435$
D) $5749.435$
E) $5399.435$

Answer 3

$5399.435$

Question 4

Evaluate the function at the indicated value of x.Round your result to three decimal places. ​
Function
Value $f ( x ) = 2000 \left( 2 ^ { x } \right)$ $x = - 1.1$ ​

A) $933.033$
B) $102.718$
C) $- 933.033$
D) $1033.033$
E) $- 102.718$

Question 5

Match the graph with its exponential function.​ ​

A) $y = 3 x$
B) $y = - 3 ^ { - x }$
C) $y = - 3 ^ { x }$
D) $y = 3 ^ { x }$
E) $y = 3 ^ { - x }$

Question 6

Use a graphing utility to construct a table of values for the function.Round your answer to three decimal places.​ $f ( x ) = e ^ { 5 x }$ ​

A) $$\begin{array} { | l | l | l | l | l | l | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline f ( x ) & 0.000 & 0.007 & - 1.000 & 148.413 & 22,026.466 \\\hline\end{array}$$
B) $$\begin{array} { | l | l | l | l | l | l | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline f ( x ) & 0.000 & 0.007 & 1.000 & - 148.413 & 22,026.466 \\\hline\end{array}$$
C) $$\begin{array} { | l | l | l | l | l | l | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline f ( x ) & 0.000 & 0.007 & 1.000 & 148.413 & 22,026.466 \\\hline\end{array}$$
D) $$\begin{array} { | l | l | l | l | l | l | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline f ( x ) & 0.000 & - 0.007 & 1.000 & 148.413 & 22,026.466 \\\hline\end{array}$$
E) $$\begin{array} { | l | l | l | l | l | l | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline f ( x ) & 0.000 & - 0.007 & - 1.000 & - 148.413 & - 22,026.466 \\\hline\end{array}$$

Question 7

Evaluate the function at the indicated value of x.Round your result to three decimal places. ​​
Function
Value $h ( x ) = 400 e ^ { 0.05 x }$ $x = 15$ ​

A) $846.800$
B) $1046.800$
C) $1246.800$
D) $946.800$
E) $1146.800$

Question 8

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

A) $$\begin{array} { | c | c | c | c | c | c | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline f ( x ) & 9.00 & 3.00 & 1.00 & 3 & - 0.11 \\\hline\end{array}$$
B) $$\begin{array} { | c | c | c | c | c | c | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline f ( x ) & - 9.00 & 3.00 & 1.00 & 3 & 0.11 \\\hline\end{array}$$
C) $$\begin{array} { | c | c | c | c | c | c | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline f ( x ) & 9.00 & - 3.00 & 1.00 & 3 & 0.11 \\\hline\end{array}$$
D) $$\begin{array} { | c | c | c | c | c | c | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline f ( x ) & 9.00 & 3.00 & 1.00 & - 3 & 0.11 \\\hline\end{array}$$
E) $$\begin{array} { | c | c | c | c | c | c | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline f ( x ) & 9.00 & 3.00 & 1.00 & 3 & 0.11 \\\hline\end{array}$$

Question 9

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

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 10

Evaluate the function at the indicated value of x.Round your result to three decimal places. ​
Function
Value $f ( x ) = 0.7 ^ { x }$ $$x = 1.7$$ ​

A) $$- 0.545$$
B) $1.7$
C) $0.545$
D) $0.7$
E) $- 1.7$

Question 11

Evaluate the function at the indicated value of x.Round your result to three decimal places. ​
Function
Value $f ( x ) = 4 ^ { x }$ $x = - \pi$ ​

A) $1.513$
B) $0.013$
C) $0.513$
D)​ $0.121$
E) $2.0129$

Question 12

Evaluate the function at the indicated value of x.Round your result to three decimal places. ​
Function
Value $h ( x ) = e ^ { - x }$ $x = \frac { 5 } { 8 }$ ​

A) $$8.07$$
B) $0.625$
C) $1.148$
D) $$5.500$$
E) $0.535$

Question 13

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

A)​ ​
B)​ ​
C)​ ​
D)​ ​
E)​ ​

Question 14

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

A)​
B)​ ​
C)​
D)​
E)​

Question 15

Select the graph of the function.​ $$f ( x ) = 2 ^ { x - 1 }$$ ​

A)​
B)​ ​
C)​
D)​
E)​

Question 16

Use a graphing utility to construct a table of values for the function.Round your answer to two decimal places.​ $$f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { x }$$ ​

A) $$\begin{array} { | c | c | c | c | c | c | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline & & & & & \\f ( x ) & 25.00 & - 5.00 & 1.00 & 0.20 & 0.04 \\\hline\end{array}$$
B) $$\begin{array} { | c | c | c | c | c | c | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline f ( x ) & 25.00 & 5.00 & - 1.00 & 0.20 & 0.04 \\\hline\end{array}$$
C) $$\begin{array} { | c | c | c | c | c | c | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline & & & & & \\f ( x ) & - 25.00 & 5.00 & 1.00 & 0.20 & 0.04 \\\hline\end{array}$$
D) $$\begin{array} { | c | c | c | c | c | c | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline f ( x ) & 25.00 & 5.00 & 1.00 & 0.20 & 0.04 \\\hline\end{array}$$
E) $$\begin{array} { | c | c | c | c | c | c | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline f ( x ) & 25.00 & 5.00 & 1.00 & - 0.20 & - 0.04 \\\hline\end{array}$$

Question 17

Match the graph with its exponential function. ​​ ​

A) $y = 5 ^ { - x } - 3$
B) $y = - 5 ^ { x } + 3$
C) $y = 5 ^ { x } + 3$
D) $y = 5 ^ { x } - 3$
E) $y = - 5 ^ { x } - 3$

Question 18

Select the graph of the exponential function.​ $$f ( x ) = 4 ^ { x + 1 } - 6$$ ​

A)​
B)​
C)​
D)​
E)​

Question 19

Evaluate the function at the indicated value of $x$ .Round your result to three decimal places. ​​
Function
Value $f ( x ) = 200 ( 1.3 ) ^ { 12 x }$ $x = 14$ ​

A) $2.504 \times 10 ^ { 2 }$
B) $4.368 \times 10 ^ { 4 }$
C) $3.048 \times 10 ^ { 36 }$
D) $1.183 \times 10 ^ { 2 }$
E) $2.777 \times 10 ^ { 21 }$

Question 20

Select the graph of the function.​ $$f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { - x }$$ ​

A)​
B)​
C)​
D)​
E)​

Question 21

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

A)​
B)​
C)​
D)​
E)​

Question 22

Select the graph of the function.​ $$f ( x ) = e ^ { 4 x }$$ ​

A)​
B)​
C)​
D)​
E)​

Question 23

Use the One-to-One Property to solve the equation for x.​ $e ^ { 6 x + 5 } = e ^ { 6 }$ ​

A) $x = - \frac { 1 } { 6 }$
B) $x ^ { 2 } = 6$
C) $x = - 6$
D) $x = \frac { 1 } { 6 }$
E) $x = 6$

Question 24

Complete the table to determine the balance A for P dollars invested at rate r for t years and compounded n times per year.​ $P = \$ 1100 ; r = 2 \% ; t = 10 \text { year }$ ​

A) $$\begin{array} { | l | l | l | l | l | l | l | } \hline n & 1 & 2 & 4 & 12 & 365 & \text { continuous } \\\hline A & \$ 1,340.89 & \$ 1342.21 & \$ 1,342.87 & \$ 1,343.32 & \$ 1,343.54 & \$ 1,343.54 \\\hline\end{array}$$
B) $$\begin{array} { | l | l | l | l | l | l | l | } \hline n & 1 & 2 & 4 & 12 & 365 & \text { continuous } \\\hline A & \$ 1,340.89 & \$ 1,343.54 & \$ 1,342.87 & \$ 1,343.32 & \$ 1,343.32 & \$ 1,343.54 \\\hline\end{array}$$
C) $$\begin{array} { | l | l | l | l | l | l | l | } \hline n & 1 & 2 & 4 & 12 & 365 & \text { continuous } \\\hline A & \$ 1,340.89 & \$ 1342.21 & \$ 1,340.89 & \$ 1,343.32 & \$ 1,343.32 & \$ 1,343.54 \\\hline\end{array}$$
D) $$\begin{array} { | l | l | l | l | l | l | l | } \hline n & 1 & 2 & 4 & 12 & 365 & \text { continuous } \\\hline A & \$ 1342.21 & \$ 1,340.89 & \$ 1,342.87 & \$ 1,343.32 & \$ 1,343.54 & \$ 1,343.54 \\\hline\end{array}$$
E) $$\begin{array} { | l | l | l | l | l | l | l | } \hline n & 1 & 2 & 4 & 12 & 365 & \text { continuous } \\\hline A & \$ 1,340.89 & \$ 1342.21 & \$ 1,342.87 & \$ 1,343.54 & \$ 1,343.32 & \$ 1,343.32 \\\hline\end{array}$$

Question 25

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

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

Question 26

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

A)​
B)​
C)​
D)​
E)​

Question 27

Select the graph of the function.​ $$f ( x ) = 4 e ^ { x + 5 }$$ ​

A)​
B)​
C)​
D)​
E)​

Question 28

After t years,the value of a wheelchair conversion van that originally cost $39,000 depreciates so that each year it is worth $\frac { 7 } { 8 }$ of its value for the previous year.Find a model for V(t),the value of the van after t years. ​

A) $V ( t ) = - 39,000 \left( - \frac { 7 } { 8 } \right) ^ { t }$
B) $V ( t ) = 39,000 \left( - \frac { 7 } { 8 } \right) ^ { t }$
C) $V ( t ) = - 39,000 \left( \frac { 7 } { 8 } \right) ^ { t }$
D) $V ( t ) = 39,000 \left( \frac { 7 } { 8 } \right) ^ { t }$
E) $V ( t ) = 39,000 \left( \frac { 7 } { 8 } \right) ^ { - t }$

Question 29

Use the One-to-One Property to solve the equation for x.​ $\left( \frac { 1 } { 2 } \right) ^ { x } = 4$ ​

A) $x = 3$
B) $x = - 2$
C) $x = 2$
D) $x = - 3$
E) $x = 4$

Question 30

Use a graphing utility to construct a table of values for the function.Round your answer to three decimal places.​ $$f ( x ) = 6 e ^ { x - 2 } + 7$$ ​

A) $$\begin{array} { | c | c | c | c | c | c | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline & - & - & & & \\f ( x ) & 7.110 & 7.299 & 7.812 & 9.207 & 13 \\\hline\end{array}$$
B) $$\begin{array} { | c | c | c | c | c | c | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline & & & & - & - \\f ( x ) & 7.110 & 7.299 & 7.812 & 9.207 & 13 \\\hline\end{array}$$
C) $$\begin{array} { | c | c | c | c | c | c | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline & & & - & & \\f ( x ) & 7.110 & 7.299 & 7.812 & 9.207 & 13 \\\hline\end{array}$$
D) $$\begin{array} { | c | c | c | c | c | c | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline f ( x ) & 7.110 & 7.299 & 7.812 & 9.207 & 13 \\\hline\end{array}$$
E) $$\begin{array} { | c | c | c | c | c | c | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline & & - & & & \\f ( x ) & 7.110 & 7.299 & 7.812 & 9.207 & 13 \\\hline\end{array}$$

Question 31

Determine whether the statement is true or false.Justify your answer. ​
The line $y = - 5$ is an asymptote for the graph of $f ( x ) = 10 ^ { x } - 5$ ​

A)False.As $x \rightarrow 5 , f ( x ) \rightarrow 5$ but never reaches 5.
B)True.As $x \rightarrow - 5 , f ( x ) \rightarrow - 5$ but never reaches -5.

Question 32

Identify the graph of the function.​ $f ( x ) = 3 - 5 ^ { x }$ ​

A)
B)
C)
D)
E)

Question 33

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

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

Question 34

Let Q represent a mass of radioactive plutonium $\left( { } ^ { 239 } \mathrm { Pu } \right)$ (in grams),whose half life is 24,100 years.The quantity of plutonium present after t years is $Q = 16 \left( \frac { 1 } { 2 } \right) ^ { t / 24,100 }$ .Determine the quantity present after 67,000 years.Round your answer to one decimal place. ​

A)4.3 g
B)3.3 g
C)5.3 g
D)2.3 g
E)6.3 g

Question 35

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

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

Question 36

Use a graphing utility to construct a table of values for the function.Round your answer to three decimal places.​ $$f ( x ) = 3 e ^ { x + 4 }$$ ​

A) $$\begin{array} { | l | l | l | l | l | l | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline & & & & & \\f ( x ) & 22.167 & 60.257 & 0 & 445.239 & 1,210.286 \\\hline\end{array}$$
B) $$\begin{array} { | l | l | l | l | l | l | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline & & - & & & \\f ( x ) & 22.167 & 60.257 & 163.792 & 445.239 & 1,210.286 \\\hline\end{array}$$
C) $$\begin{array} { | l | l | l | l | l | l | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline & & & & & \\f ( x ) & 22.167 & 60.257 & 163.792 & 445.239 & 1,210.286 \\\hline\end{array}$$
D) $$\begin{array} { | l | l | l | l | l | l | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline & - & & & & \\f ( x ) & 22.167 & 60.257 & 163.792 & 445.239 & 1,210.286 \\\hline\end{array}$$
E) $$\begin{array} { | l | l | l | l | l | l | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline & - & - & & & \\f ( x ) & 22.167 & 60.257 & 163.792 & 445.239 & 1,210.286 \\\hline\end{array}$$

Question 37

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

A)​
B)​ ​
C)​
D)​
E)​

Question 38

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

A)​
B)​ ​
C)​
D)​
E)​

Question 39

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

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

Question 40

Use the One-to-One Property to solve the equation for x.​ $$5 ^ { x + 1 } = 25$$ ​

A) $$x = 5$$
B) $$x = 1$$
C) $$x = 4$$
D) $$x = 2$$
E) $x = 3$

Question 41

Identify the graph of the function.​ $$f ( x ) = \left( \frac { 1 } { 7 } \right) ^ { x }$$

A)
B)
C)
D)
E)

Question 42

Use a graphing utility to determine which graph below is the graph of the function.​ $s ( x ) = 1.1 e ^ { - ( x - 1 ) ^ { 2 } }$

A)
B)
C)
D)
E)

Question 43

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

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

Question 44

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

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

Question 45

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

A)
B)​
C)
D)
E)

Question 46

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

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

Question 47

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

A)
B)
C)
D)

Question 48

What is the value of the function $f ( x ) = 150 e ^ { 0.4 x }$ at $x = 2.3$ ? Round to 3 decimal places.

A)376.394
B)223.774
C)18.232
D)151.492
E)1247.646

Question 49

Graph the function using translations.​ $$f ( x ) = e ^ { x + 1 } + 2$$ ​

A)
B)
C)
D)

Question 50

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.

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

Question 51

Sketch the graph of the function
​​ ​

Question 52

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

A) $b = \frac { 1 } { e ^ { 3 } }$
B) $b = e ^ { 3 }$
C) $b = e$
D) $b = \frac { 1 } { e }$
E) $b = e ^ { 2 }$

Question 53

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

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

Question 54

Sketch the graph of the function.​ $f ( x ) = 2 - 2 ^ { x }$ ​

A)​
B)​
C)​
D)​
E)​

Question 55

Evaluate the function $$f ( x ) = 1.3 ^ { x }$$ at $x = 3.6$ .Round to 3 decimal places.

A)5.287
B)4.680
C)20.055
D)2.572
E)1.690

Question 56

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

A)
B)
C)
D)

Question 57

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

A)
B)
C)
D)

Question 58

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

A)
B)
C)
D)

Question 59

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

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