Question 1

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.

Accepted Answer

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

Question 2

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(12) t/1599Q = 5 \left( \frac { 1 } { 2 } \right)  ^ { t / 1599 }Q=5(21​) 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

Question 3

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

Accepted Answer

A)  ​ 
B)  ​ 
C)  ​ 
D)  ​ 
E)  ​

Question 4

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  ​

Accepted Answer

A)   
B)  ​ 
C)   
D)   
E)

Question 5

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

Accepted Answer

A)   
B)   
C)   
D)

Question 6

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

Accepted Answer

A)   
B)   
C)   
D)

Question 7

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

Accepted Answer

A)  ​ 
B)  ​  ​
C)  ​ 
D)  ​ 
E)  ​

Question 8

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.

Accepted Answer

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

Question 9

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  ​

Accepted Answer

A)    x−2−1012f(x) 2.132.252.503.004.00\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}xf(x) ​−22.13​−12.25​02.50​13.00​24.00​​ 
B)    x−2−1012f(x) 2.132.25−2.503.004.00\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}xf(x) ​−22.13​−12.25​0−2.50​13.00​24.00​​ 
C)    x−2−1012f(x) 2.13−2.252.503.004.00\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}xf(x) ​−22.13​−1−2.25​02.50​13.00​24.00​​ 
D)    x−2−1012f(x) 2.132.252.50−3.00−4.00\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}xf(x) ​−22.13​−12.25​02.50​1−3.00​2−4.00​​ 
E)    x−2−1012f(x) −2.132.252.503.004.00\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}xf(x) ​−2−2.13​−12.25​02.50​13.00​24.00​​

Question 10

Use properties of exponents to determine which functions (if any) are the same.​  f(x) =6x−2g(x) =6x−36f(x) =136(6x) \begin{array} { l } f ( x )  = 6 ^ { x - 2 } \g ( x )  = 6 ^ { x } - 36 \f ( x )  = \frac { 1 } { 36 } \left( 6 ^ { x } ight) \end{array}f(x) =6x−2g(x) =6x−36f(x) =361​(6x) ​  ​

Accepted Answer

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

Question 11

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.

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

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  ​

Accepted Answer

A)    12\frac { 1 } { 2 }21​ 
B)    −14- \frac { 1 } { 4 }−41​ 
C)    13\frac { 1 } { 3 }31​ 
D)    −38- \frac { 3 } { 8 }−83​ 
E)    18\frac { 1 } { 8 }81​

Question 14

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

Accepted Answer

A)    73\frac { 7 } { 3 }37​ 
B)    37\frac { 3 } { 7 }73​ 
C)    1283\frac { 128 } { 3 }3128​ 
D)  2
E)    −643- \frac { 64 } { 3 }−364​

Question 15

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

Accepted Answer

A)  ​ 
B)  ​  ​
C)  ​ 
D)  ​ 
E)  ​

Question 16

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.

Accepted Answer

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

Question 17

Match the graph with its exponential function.​  ​

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

Find the value of b that would cause the graph of y = bx to look like the graph indicated.​ 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 }" class="answers-bank-image d-inline" rel="preload" > ​

Accepted Answer

A)    b=14b = \frac { 1 } { 4 }b=41​ 
B)    b=34b = \frac { 3 } { 4 }b=43​ 
C)    b=4b = 4b=4 
D)    b=−4b = - 4b=−4 
E)    b=−14b = - \frac { 1 } { 4 }b=−41​

Exam 18: Exponential Functions and Their Graphs

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

Correct Answer
verified

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.

Correct Answer
verified

Find the value of b that would cause the graph of y = b^x to look like the graph indicated. $Find the value of b that would cause the graph of y = b<sup>x</sup> to look like the graph indicated. A) b = \frac { 1 } { 4 } B) b = \frac { 3 } { 4 } C) b = 4 D) b = - 4 E) b = - \frac { 1 } { 4 }$

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

Match the graph with its exponential function. $Match the graph with its exponential function. A) y = 4 ^ { x } B) y = - 4 ^ { - x } C) y = - 4 ^ { x } D) y = 4 ^ { - x } E) y = 4 x$

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

Exam 18: Exponential Functions and Their Graphs

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

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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.

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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 ​

Correct AnswerverifiedShow Answer

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.

Correct AnswerverifiedShow Answer

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.

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Match the graph with its exponential function.​ ​

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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.

Correct AnswerverifiedShow Answer

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 ​

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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 ​

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

Correct Answer
verified

Correct Answer
verified

Find the value of b that would cause the graph of y = b^x to look like the graph indicated. $Find the value of b that would cause the graph of y = b<sup>x</sup> to look like the graph indicated. A) b = \frac { 1 } { 4 } B) b = \frac { 3 } { 4 } C) b = 4 D) b = - 4 E) b = - \frac { 1 } { 4 }$

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

Correct Answer
verified

Match the graph with its exponential function. $Match the graph with its exponential function. A) y = 4 ^ { x } B) y = - 4 ^ { - x } C) y = - 4 ^ { x } D) y = 4 ^ { - x } E) y = 4 x$

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified