Question 1

Find the logistic function f with the given properties. f has limiting value 18 and passes through (0, 9) and (1, 16).

Accepted Answer

A)  $f ( x ) = \frac { 1 } { 1 + 2 \left( 8 ^ { - x } \right) }$ 
B)    $f ( x ) = \frac { 18 } { 1 + 2 \left( 16 ^ { - x } \right) }$ 
C)   $f ( x ) = \frac { 18 } { 1 + \left( 8 ^ { - x } \right) }$ 
D)    $f ( x ) = \frac { 9 } { 1 + \left( 8 ^ { - x } \right) }$ 
E)    $f ( x ) = \frac { 18 } { 1 + \left( 16 ^ { - x } \right) }$ 
A)  $f ( x ) = \frac { 1 } { 1 + 2 \left( 8 ^ { - x } \right) }$ 
B)    $f ( x ) = \frac { 18 } { 1 + 2 \left( 16 ^ { - x } \right) }$ 
C)   $f ( x ) = \frac { 18 } { 1 + \left( 8 ^ { - x } \right) }$ 
D)    $f ( x ) = \frac { 9 } { 1 + \left( 8 ^ { - x } \right) }$ 
E)    $f ( x ) = \frac { 18 } { 1 + \left( 16 ^ { - x } \right) }$

Question 2

Choose the logistic function that best approximates the given curve.

Accepted Answer

A)  $f ( x ) = \frac { 10 } { 1 + 9 \left( 5 ^ { - x } \right) }$ 
B)    $f ( x ) = \frac { 10 } { 1 + 4 \left( 5 ^ { - x } \right) }$ 
C)    $f ( x ) = \frac { 10 } { 1 + 4 \left( 0.5 ^ { - x } \right) }$ 
D)    $f ( x ) = \frac { 10 } { 1 + 6 \left( 0.5 ^ { - x } \right) }$ 
E)    $f ( x ) = \frac { 10 } { 1 + 9 \left( 0.5 ^ { - x } \right) }$ 
A)  $f ( x ) = \frac { 10 } { 1 + 9 \left( 5 ^ { - x } \right) }$ 
B)    $f ( x ) = \frac { 10 } { 1 + 4 \left( 5 ^ { - x } \right) }$ 
C)    $f ( x ) = \frac { 10 } { 1 + 4 \left( 0.5 ^ { - x } \right) }$ 
D)    $f ( x ) = \frac { 10 } { 1 + 6 \left( 0.5 ^ { - x } \right) }$ 
E)    $f ( x ) = \frac { 10 } { 1 + 9 \left( 0.5 ^ { - x } \right) }$

Question 3

The fuel efficiency (in miles per gallon) of a sport utility vehicle (SUV) depends on its weight according to the formula  
 $E = 0.00005 x ^ { 2 } - 0.3 x + 41$  
Where x is the weight of an SUV in pounds. According to the model, what is the weight of the least fuel-efficient SUV

Accepted Answer

A) 3,000 pounds 
B)  3,100 pounds 
C)  2,000 pounds 
D)  6,000 pounds 
E)  491 pounds 
A) 3,000 pounds 
B)  3,100 pounds 
C)  2,000 pounds 
D)  6,000 pounds 
E)  491 pounds

Question 4

The given table corresponds to the function $$f ( x ) = e ^ { \frac { x } { 5 } }$$ . $$\begin{array} { | l | l | l | l | l | l | l | l | } 
\hline \boldsymbol { x } & - 3 & - 2 & - 1 & 0 & 1 & 2 & 3 \
\hline \boldsymbol { f } ( \boldsymbol { x } ) & 0.549 & 0.67 & 0.819 & 1 & 1.221 & 1.492 & 1.822 \
\hline
\end{array}$$

Accepted Answer

A) True 
 B)False

Question 5

The U.S. population was 170 million in 1970 and 250 million in 1995. Assuming exponential population growth, what will the population be in the year 2025 
 
Round your answer to the nearest million.
 
__________ million

Accepted Answer

The answer of The U.S. population was 170 million in...

Question 6

How long, to the nearest year, will it take an investment in U.S. to double its value if the interest is compounded every six months  Please round the answer to the nearest year. $$\begin{array} { | l | l | l | l | l | l | } 
\hline \text { Country } & \text { U.S. } & \text { Japan } & \text { Canada } & \text { Korea } & \text { Australia } \
\hline \text { Yield } & 5.3 \% & 1.5 \% & 5.2 \% & 5.4 \% & 6.0 \% \
\hline
\end{array}$$

Accepted Answer

A) 14 years 
B)  16 years 
C)  13 years 
D)  8 years 
E)  15 years 
A) 14 years 
B)  16 years 
C)  13 years 
D)  8 years 
E)  15 years

Question 7

Rock Solid Bank & Trust is offering a CD that pays 5% compounded continuously. How much interest would a $1,000 deposit earn over 12 years  (Round your answer to the nearest dollar.)  
Select the correct answer.

Accepted Answer

A) $2,822 
B)  $822 
C)  $1,822 
D)  $1,820 
E)  $1,796 
A) $2,822 
B)  $822 
C)  $1,822 
D)  $1,820 
E)  $1,796

Question 8

Choose the logistic function that best approximates the curve.

Accepted Answer

A)  $f ( x ) = \frac { 10 } { 1 + 1.5 \left( 3 ^ { - x } \right) }$ 
B)  $f ( x ) = \frac { 9 } { 1 + 3.5 \left( 2 ^ { - x } \right) }$ 
C)  $f ( x ) = \frac { 10 } { 1 + 1.5 \left( 1.05 ^ { - x } \right) }$ 
A)  $f ( x ) = \frac { 10 } { 1 + 1.5 \left( 3 ^ { - x } \right) }$ 
B)  $f ( x ) = \frac { 9 } { 1 + 3.5 \left( 2 ^ { - x } \right) }$ 
C)  $f ( x ) = \frac { 10 } { 1 + 1.5 \left( 1.05 ^ { - x } \right) }$

Question 9

The market research department of the Better Baby Buggy Co. predicts that the demand equation for its buggies is given by 
$q = - 0.5 x + 170$ where q is the number of buggies it can sell in a month if the price is $x per buggy. What is the largest monthly revenue  Round your answer to the nearest dollar.

Accepted Answer

A) $85 
B)  $14,450 
C)  $170 
D)  $7,225 
E)  $28,900 
A) $85 
B)  $14,450 
C)  $170 
D)  $7,225 
E)  $28,900

Question 10

The given table corresponds to the function $$f ( x ) = 5 ^ { x } - 1$$ . $$\begin{array} { | l | l | l | l | l | l | l | l | } 
\hline \boldsymbol { x } & - 3 & - 2 & - 1 & 0 & 1 & 2 & 3 \
\hline \boldsymbol { f } ( \boldsymbol { x } ) & - 0.992 & - 0.96 & - 0.8 & 0 & 4 & 24 & 124 \
\hline
\end{array}$$

Accepted Answer

A) True 
 B)False

Question 11

Choose the correct letter for each question.
​
-2, 4

Accepted Answer

A) $x ^ { 2 } - 6 x + 8$ 
B) $x ^ { 2 } + 10 x + 25$ 
C) $x ^ { 2 } + 10 x + 30$ 
A) $x ^ { 2 } - 6 x + 8$ 
B) $x ^ { 2 } + 10 x + 25$ 
C) $x ^ { 2 } + 10 x + 30$

Question 12

The table below is filled correctly. $$\begin{array} { | l | l | } 
\hline \text { Exponential form } & \text { Logarithmic form } \
\hline 5 ^ { 1 } = 5 & \log _ { 5 } 5 = 1 \
\hline 7 ^ { 4 } = 2,401 & \log _ { 7 } 2,401 = 4 \
\hline 9 ^ { - 1 } = \frac { 1 } { 9 } & \log _ { 9 } \frac { 1 } { 9 } = - 1 \
\hline 10 ^ { 3 } = 1,000 & \log _ { 10 } 1,000 = 3 \
\hline
\end{array}$$

Accepted Answer

A) True 
 B)False

Question 13

Model the data using an exponential function $$f ( x ) = A b ^ { x }$$ . $$\begin{array} { | l | l | l | } 
\hline \boldsymbol { x } & 1 & 2 \
\hline f ( x ) & 13 & 16.9 \
\hline
\end{array}$$   Select the correct answer.

Accepted Answer

A)  $f ( x ) = 10 ( 10 ) ^ { x }$ 
B)  $f ( x ) = 1.3 ( 1.3 ) ^ { - x }$ 
C)  $f ( x ) = 10 ( 1.3 ) ^ { x }$ 
D)  $f ( x ) = 10 ( 1.3 ) ^ { - x }$ 
E)  $f ( x ) = 1.3 ( 10 ) ^ { x }$ 
A)  $f ( x ) = 10 ( 10 ) ^ { x }$ 
B)  $f ( x ) = 1.3 ( 1.3 ) ^ { - x }$ 
C)  $f ( x ) = 10 ( 1.3 ) ^ { x }$ 
D)  $f ( x ) = 10 ( 1.3 ) ^ { - x }$ 
E)  $f ( x ) = 1.3 ( 10 ) ^ { x }$

Question 14

There are currently 1,000 cases of Venusian flu in a total susceptible population of 10,000 and the number of cases is increasing by 25% each day. Find a logistic model for the number of cases of Venusian flu and use your model to predict the number of flu cases a week from now. Round your answer to the nearest integer.

Accepted Answer

A)  $F ( 7 ) = 1,732$ cases 
B)  $F ( 7 ) = 5,195$ cases 
C)  $F ( 7 ) = 3,463$ cases 
D)  $F ( 7 ) = 5,888$ cases 
E)  $F ( 7 ) = 1,154$ cases 
A)  $F ( 7 ) = 1,732$ cases 
B)  $F ( 7 ) = 5,195$ cases 
C)  $F ( 7 ) = 3,463$ cases 
D)  $F ( 7 ) = 5,888$ cases 
E)  $F ( 7 ) = 1,154$ cases

Question 15

Choose the logistic function that best approximates the curve.

Accepted Answer

A)  $f ( x ) = \frac { 8 } { 1 + 7 ( 0.5 ) ^ { - x } }$ 
B)  $f ( x ) = \frac { 8 } { 1 + 3 ( 0.5 ) ^ { - x } }$ 
C)  $f ( x ) = \frac { 8 } { 1 + 3 ( 3 ) ^ { - x } }$ 
A)  $f ( x ) = \frac { 8 } { 1 + 7 ( 0.5 ) ^ { - x } }$ 
B)  $f ( x ) = \frac { 8 } { 1 + 3 ( 0.5 ) ^ { - x } }$ 
C)  $f ( x ) = \frac { 8 } { 1 + 3 ( 3 ) ^ { - x } }$

Question 16

Find the equation for the exponential function that passes through the pair of points $( 2,4 )$ and $( 7,1 )$ .
​ $y = A b ^ { x } ( b > 0 )$ ​
A = __________
​
b = __________
​
Round your answer to four decimal places.

Accepted Answer

The answer of Find the equation for the exponential function...

Question 17

The given table corresponds to the function $f ( x ) = 10 ^ { x - 1 }$ . $\begin{array} { | l | l | l | l | l | l | l | l | } 
\hline \boldsymbol { x } & - 3 & - 2 & - 1 & 0 & 1 & 2 & 3 \
\hline \boldsymbol { f } ( \boldsymbol { x } ) & 0.0001 & 0.001 & 0.01 & 0.1 & 1 & 10 & 100 \
\hline
\end{array}$

Accepted Answer

A) True 
 B)False

Question 18

Choose the logistic function that best approximates the given curve.

Accepted Answer

A)  $f ( x ) = \frac { 10 } { 1 + 0.5 \left( 1.01 ^ { - x } \right) }$ 
B)  $f ( x ) = \frac { 10 } { 1 + 4 \left( 2 ^ { - x } \right) }$ 
C)    $f ( x ) = \frac { 6 } { 1 + 4 \left( 3 ^ { - x } \right) }$ 
D)    $f ( x ) = \frac { 6 } { 1 + 0.5 \left( 2 ^ { - x } \right) }$ 
E)    $f ( x ) = \frac { 6 } { 1 + 0.5 \left( 3 ^ { - x } \right) }$ 
A)  $f ( x ) = \frac { 10 } { 1 + 0.5 \left( 1.01 ^ { - x } \right) }$ 
B)  $f ( x ) = \frac { 10 } { 1 + 4 \left( 2 ^ { - x } \right) }$ 
C)    $f ( x ) = \frac { 6 } { 1 + 4 \left( 3 ^ { - x } \right) }$ 
D)    $f ( x ) = \frac { 6 } { 1 + 0.5 \left( 2 ^ { - x } \right) }$ 
E)    $f ( x ) = \frac { 6 } { 1 + 0.5 \left( 3 ^ { - x } \right) }$

Question 19

Find the logistic function f with the given properties. f has limiting value 12 and passes through (0, 3) and (1, 10).

Accepted Answer

A)  $f ( x ) = \frac { 12 } { 1 + 4 \left( 30 ^ { - x } \right) }$ 
B)    $f ( x ) = \frac { 12 } { 1 + 3 \left( 15 ^ { - x } \right) }$ 
C)    $f ( x ) = \frac { 3 } { 1 + 3 \left( 30 ^ { - x } \right) }$ 
D)    $f ( x ) = \frac { 3 } { 1 + 3 \left( 15 ^ { - x } \right) }$ 
E)    $f ( x ) = \frac { 12 } { 1 + 3 \left( 30 ^ { - x } \right) }$ 
A)  $f ( x ) = \frac { 12 } { 1 + 4 \left( 30 ^ { - x } \right) }$ 
B)    $f ( x ) = \frac { 12 } { 1 + 3 \left( 15 ^ { - x } \right) }$ 
C)    $f ( x ) = \frac { 3 } { 1 + 3 \left( 30 ^ { - x } \right) }$ 
D)    $f ( x ) = \frac { 3 } { 1 + 3 \left( 15 ^ { - x } \right) }$ 
E)    $f ( x ) = \frac { 12 } { 1 + 3 \left( 30 ^ { - x } \right) }$

Question 20

For the following demand equation, express the total revenue R as a function of the price p per item.  $q = - 2 p + 1600$

Accepted Answer

A)  $R = - 2 p ^ { 2 } + 1600 p$ 
B)  $R = - 2 p ^ { 2 } + 1600$ 
C)  $R = 1598 p$ 
D)  $R = - 2 + \frac { 1600 } { p }$ 
E)  $R = - 2 p ^ { 2 }$ 
A)  $R = - 2 p ^ { 2 } + 1600 p$ 
B)  $R = - 2 p ^ { 2 } + 1600$ 
C)  $R = 1598 p$ 
D)  $R = - 2 + \frac { 1600 } { p }$ 
E)  $R = - 2 p ^ { 2 }$

Find the logistic function f with the given properties. f has limiting value 18 and passes through (0, 9) and (1, 16).

Choose the logistic function that best approximates the given curve.

The fuel efficiency (in miles per gallon) of a sport utility vehicle (SUV) depends on its weight according to the formula $E = 0.00005 x ^ { 2 } - 0.3 x + 41$ Where x is the weight of an SUV in pounds. According to the model, what is the weight of the least fuel-efficient SUV

The given table corresponds to the function $f ( x ) = e ^ { \frac { x } { 5 } }$ . -3 -2 -1 0 1 2 3 ( ) 0.549 0.67 0.819 1 1.221 1.492 1.822

The U.S. population was 170 million in 1970 and 250 million in 1995. Assuming exponential population growth, what will the population be in the year 2025 Round your answer to the nearest million. __________ million

How long, to the nearest year, will it take an investment in U.S. to double its value if the interest is compounded every six months Please round the answer to the nearest year. Country U.S. Japan Canada Korea Australia Yield 5.3\% 1.5\% 5.2\% 5.4\% 6.0\%

Rock Solid Bank & Trust is offering a CD that pays 5% compounded continuously. How much interest would a $1,000 deposit earn over 12 years (Round your answer to the nearest dollar.) Select the correct answer.

Choose the logistic function that best approximates the curve.

The given table corresponds to the function $f ( x ) = 5 ^ { x } - 1$ . -3 -2 -1 0 1 2 3 ( ) -0.992 -0.96 -0.8 0 4 24 124

Choose the correct letter for each question. -2, 4

The table below is filled correctly. Exponential form Logarithmic form =5 5=1 =2,401 2,401=4 = =-1 1=1,000 1,000=3

Model the data using an exponential function $f ( x ) = A b ^ { x }$ . 1 2 f(x) 13 16.9 Select the correct answer.

Choose the logistic function that best approximates the curve.

Find the equation for the exponential function that passes through the pair of points $( 2,4 )$ and $( 7,1 )$ . $y = A b ^ { x } ( b > 0 )$ A = b = Round your answer to four decimal places.

The given table corresponds to the function $f ( x ) = 10 ^ { x - 1 }$ . -3 -2 -1 0 1 2 3 ( ) 0.0001 0.001 0.01 0.1 1 10 100

Choose the logistic function that best approximates the given curve.

Find the logistic function f with the given properties. f has limiting value 12 and passes through (0, 3) and (1, 10).

For the following demand equation, express the total revenue R as a function of the price p per item. $q = - 2 p + 1600$

Functions and Applications

The Mathematics of Finance

Systems of Linear Equations and Matrices

Matrix Algebra and Applications

Linear Programming

Sets and Counting

Probability

Random Variables and Statistics

Introduction to the Derivative

Techniques of Differentiation

Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters

Exam 2: Nonlinear Functions and Models

Find the logistic function f with the given properties. f has limiting value 18 and passes through (0, 9) and (1, 16).

Choose the logistic function that best approximates the given curve.

The given table corresponds to the function f(x)=ex5f ( x ) = e ^ { \frac { x } { 5 } }f(x)=e5x​ . -3 -2 -1 0 1 2 3 ( ) 0.549 0.67 0.819 1 1.221 1.492 1.822

The U.S. population was 170 million in 1970 and 250 million in 1995. Assuming exponential population growth, what will the population be in the year 2025 Round your answer to the nearest million. __________ million

How long, to the nearest year, will it take an investment in U.S. to double its value if the interest is compounded every six months Please round the answer to the nearest year. Country U.S. Japan Canada Korea Australia Yield 5.3\% 1.5\% 5.2\% 5.4\% 6.0\%

Rock Solid Bank & Trust is offering a CD that pays 5% compounded continuously. How much interest would a $1,000 deposit earn over 12 years (Round your answer to the nearest dollar.) Select the correct answer.

Choose the logistic function that best approximates the curve.

The given table corresponds to the function f(x)=5x−1f ( x ) = 5 ^ { x } - 1f(x)=5x−1 . -3 -2 -1 0 1 2 3 ( ) -0.992 -0.96 -0.8 0 4 24 124

Choose the correct letter for each question. ​ -2, 4

The table below is filled correctly. Exponential form Logarithmic form =5 5=1 =2,401 2,401=4 = =-1 1=1,000 1,000=3

Model the data using an exponential function f(x)=Abxf ( x ) = A b ^ { x }f(x)=Abx . 1 2 f(x) 13 16.9 Select the correct answer.

Choose the logistic function that best approximates the curve.

Find the equation for the exponential function that passes through the pair of points (2,4)( 2,4 )(2,4) and (7,1)( 7,1 )(7,1) . ​ y=Abx(b>0)y = A b ^ { x } ( b > 0 )y=Abx(b>0) ​ A = __________ ​ b = __________ ​ Round your answer to four decimal places.

The given table corresponds to the function f(x)=10x−1f ( x ) = 10 ^ { x - 1 }f(x)=10x−1 . -3 -2 -1 0 1 2 3 ( ) 0.0001 0.001 0.01 0.1 1 10 100

Choose the logistic function that best approximates the given curve.

Find the logistic function f with the given properties. f has limiting value 12 and passes through (0, 3) and (1, 10).

For the following demand equation, express the total revenue R as a function of the price p per item. q=−2p+1600q = - 2 p + 1600q=−2p+1600

Functions and Applications

The Mathematics of Finance

Systems of Linear Equations and Matrices

Matrix Algebra and Applications

Linear Programming

Sets and Counting

Probability

Random Variables and Statistics

Introduction to the Derivative

Techniques of Differentiation

Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters

The given table corresponds to the function $f ( x ) = e ^ { \frac { x } { 5 } }$ . -3 -2 -1 0 1 2 3 ( ) 0.549 0.67 0.819 1 1.221 1.492 1.822

The given table corresponds to the function $f ( x ) = 5 ^ { x } - 1$ . -3 -2 -1 0 1 2 3 ( ) -0.992 -0.96 -0.8 0 4 24 124

Choose the correct letter for each question. -2, 4

Model the data using an exponential function $f ( x ) = A b ^ { x }$ . 1 2 f(x) 13 16.9 Select the correct answer.

Find the equation for the exponential function that passes through the pair of points $( 2,4 )$ and $( 7,1 )$ . $y = A b ^ { x } ( b > 0 )$ A = b = Round your answer to four decimal places.

The given table corresponds to the function $f ( x ) = 10 ^ { x - 1 }$ . -3 -2 -1 0 1 2 3 ( ) 0.0001 0.001 0.01 0.1 1 10 100

For the following demand equation, express the total revenue R as a function of the price p per item. $q = - 2 p + 1600$