Question 1

For the given function write limit notation for the end behavior.

Accepted Answer

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

Question 2

The total cost for producing   units of a commodity is $4.8 million, and the revenue generated by the sale of   units is $7.4 million. What is the profit on   units of the commodity?

Accepted Answer

A)  $12.2 million 
B)  $1.5 million 
C)  $2.6 million 
D)  $4.8 million 
E)  $7.4 million 
A)  $12.2 million 
B)  $1.5 million 
C)  $2.6 million 
D)  $4.8 million 
E)  $7.4 million

Question 3

The percentage of mothers in a large city who gave birth to a child in 2005 and returned to the workforce within x months of having the child is modeled as   percent What percentage of mothers returned to the workforce within the first year after giving birth?
Round to the nearest thousandth.

Accepted Answer

A)  51.222% 
B)  28.435% 
C)  36.925% 
D)  38.980% 
E)  25.272% 
A)  51.222% 
B)  28.435% 
C)  36.925% 
D)  38.980% 
E)  25.272%

Question 4

How much money would you have to invest today at 6% APR compounded monthly to accumulate the sum of $270,000 in 37 years? Round to the nearest hundredth.

Accepted Answer

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

Question 5

Rewrite the following pair of functions as one composite function.   ;

Accepted Answer

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

Question 6

What is the period of the following function?

Accepted Answer

A)  14 
B)  56 
C)  2 
D)  9 
E)  11 
A)  14 
B)  56 
C)  2 
D)  9 
E)  11

Question 7

Find the input of the function   corresponding to the output   .

Accepted Answer

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

Question 8

Find the input of the function   corresponding to the output   to three decimal places.

Accepted Answer

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

Question 9

Use properties of limits and algebraic methods to find the limit, if it exists.

Accepted Answer

A)    
B)    
C)    
D)    
E)  does not exist 
A)    
B)    
C)    
D)    
E)  does not exist

Question 10

The table gives the percent of the population of a certain city that was foreign born in the given year. Find a cubic function that best fits the data where x is the number of years after 1900 and y is equal to the percent. By trial and error, estimate the year the model predicts that the foreign-born population will be 100%.

Accepted Answer

A)    foreign born population will be 100% in 1965. 
B)    foreign born population will be 100% in 1975. 
C)    foreign born population will be 100% in 1975. 
D)    foreign born population will be 100% in 1965. 
E)    foreign born population will be 100% in 1985. 
A)    foreign born population will be 100% in 1965. 
B)    foreign born population will be 100% in 1975. 
C)    foreign born population will be 100% in 1975. 
D)    foreign born population will be 100% in 1965. 
E)    foreign born population will be 100% in 1985.

Question 11

In 1990, there were 2 women among the CEOs of Fortune 500 companies. In 2009, this number had risen to 18 women. What was the percentage change in the number of Fortune 500 women CEOs between 1990 and 2009?

Accepted Answer

A)  800% 
B)  8% 
C)  180% 
D)  20% 
E)  91% 
A)  800% 
B)  8% 
C)  180% 
D)  20% 
E)  91%

Question 12

Indicate whether the function is an increasing or decreasing logistic function and identify the upper limiting value of the function

Accepted Answer

A)  The function is increasing and the upper limit is 18.00. 
B)  The function is decreasing and the upper limit is 18.00. 
C)  The function is increasing and the upper limit is 68.00. 
D)  The function is decreasing and the upper limit is 68.00. 
E)  The function is decreasing and the upper limit is 0.00. 
A)  The function is increasing and the upper limit is 18.00. 
B)  The function is decreasing and the upper limit is 18.00. 
C)  The function is increasing and the upper limit is 68.00. 
D)  The function is decreasing and the upper limit is 68.00. 
E)  The function is decreasing and the upper limit is 0.00.

Question 13

Use properties of limits and algebraic methods to find the limit, if it exists.

Accepted Answer

A)    
B)    
C)    
D)    
E)  does not exist 
A)    
B)    
C)    
D)    
E)  does not exist

Question 14

To offset college expenses, at the beginning of your freshman year you obtain a nonsubsidized student loan for $18,000. Interest on this loan accrues at a rate of 3.15% compounded monthly. However, you do not have to make any payments against either the principal or the interest until after you graduate. Write a model giving the total amount you will owe on this loan after t years in college.

Accepted Answer

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

Question 15

How long would it take an investment to double if the interest rate is 4.2%, compounded monthly? Round your answer to two decimal places.

Accepted Answer

A)  16.85 years 
B)  0.48 year 
C)  17.68 years 
D)  16.53 years 
E)  1.38 years 
A)  16.85 years 
B)  0.48 year 
C)  17.68 years 
D)  16.53 years 
E)  1.38 years

Question 16

Complete the table and use it to predict the limit, if it exists.

Accepted Answer

A)    
B)    
C)    
D)    
E)  does not exist 
A)    
B)    
C)    
D)    
E)  does not exist

Question 17

Indicate whether the function is an increasing or decreasing logistic function and identify the upper limiting value of the function   .

Accepted Answer

A)  The function is decreasing and the upper limit is 2.7. 
B)  The function is decreasing and the upper limit is -0.4. 
C)  The function is decreasing and the upper limit is 0.4. 
D)  The function is increasing and the upper limit is 4.2. 
E)  The function is increasing and the upper limit is 0.0. 
A)  The function is decreasing and the upper limit is 2.7. 
B)  The function is decreasing and the upper limit is -0.4. 
C)  The function is decreasing and the upper limit is 0.4. 
D)  The function is increasing and the upper limit is 4.2. 
E)  The function is increasing and the upper limit is 0.0.

Question 18

Calculate the average rate of change in the population (in people per month) between April, 1999, and July, 2001.

Accepted Answer

A)  -3548 people per month 
B)  -3992 people per month 
C)  -19,160 people per month 
D)  -2903 people per month 
E)  -8709 people per month 
A)  -3548 people per month 
B)  -3992 people per month 
C)  -19,160 people per month 
D)  -2903 people per month 
E)  -8709 people per month

Question 19

The following table gives the percent of the U.S. population with Internet connections for the years 1997 to 2003. Use a calculator to find the logistic function that models these data. Use x as the number of years past 1995.   Source: U.S. Department of Commerce

Accepted Answer

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

Question 20

Use the formula   to find the doubling time t, in years, for an investment at r% compounded n times per year. Suppose you make an investment of $1300 at interest rate 12% compounded quarterly. How long will it take for your investment to double?

Accepted Answer

A)  3.06 years 
B)  1.95 years 
C)  11.72 years 
D)  0.76 years 
E)  5.86 years 
A)  3.06 years 
B)  1.95 years 
C)  11.72 years 
D)  0.76 years 
E)  5.86 years

For the given function write limit notation for the end behavior.

The total cost for producing units of a commodity is $4.8 million, and the revenue generated by the sale of units is $7.4 million. What is the profit on units of the commodity?

The percentage of mothers in a large city who gave birth to a child in 2005 and returned to the workforce within x months of having the child is modeled as percent What percentage of mothers returned to the workforce within the first year after giving birth? Round to the nearest thousandth.

How much money would you have to invest today at 6% APR compounded monthly to accumulate the sum of $270,000 in 37 years? Round to the nearest hundredth.

Rewrite the following pair of functions as one composite function. ;

What is the period of the following function?

Find the input of the function corresponding to the output .

Find the input of the function corresponding to the output to three decimal places.

Use properties of limits and algebraic methods to find the limit, if it exists.

In 1990, there were 2 women among the CEOs of Fortune 500 companies. In 2009, this number had risen to 18 women. What was the percentage change in the number of Fortune 500 women CEOs between 1990 and 2009?

Indicate whether the function is an increasing or decreasing logistic function and identify the upper limiting value of the function

Use properties of limits and algebraic methods to find the limit, if it exists.

How long would it take an investment to double if the interest rate is 4.2%, compounded monthly? Round your answer to two decimal places.

Complete the table and use it to predict the limit, if it exists.

Indicate whether the function is an increasing or decreasing logistic function and identify the upper limiting value of the function .

Calculate the average rate of change in the population (in people per month) between April, 1999, and July, 2001.

The following table gives the percent of the U.S. population with Internet connections for the years 1997 to 2003. Use a calculator to find the logistic function that models these data. Use x as the number of years past 1995. Source: U.S. Department of Commerce

Use the formula to find the doubling time t, in years, for an investment at r% compounded n times per year. Suppose you make an investment of $1300 at interest rate 12% compounded quarterly. How long will it take for your investment to double?

Describing Change: Rates

Determining Change: Derivatives

Analyzing Change: Applications of Derivatives

Accumulating Change: Limits of Sums and the Definite Integral

Analyzing Accumulated Change: Integrals in Action

Ingredients of Multivariable Change: Models, Graphs, Rates

Analyzing Multivariable Change: Optimization

Filters

Exam 1: Ingredients of Change: Functions an Limits

For the given function write limit notation for the end behavior.

The total cost for producing units of a commodity is $4.8 million, and the revenue generated by the sale of units is $7.4 million. What is the profit on units of the commodity?

The percentage of mothers in a large city who gave birth to a child in 2005 and returned to the workforce within x months of having the child is modeled as percent What percentage of mothers returned to the workforce within the first year after giving birth? Round to the nearest thousandth.

How much money would you have to invest today at 6% APR compounded monthly to accumulate the sum of $270,000 in 37 years? Round to the nearest hundredth.

Rewrite the following pair of functions as one composite function. ;

What is the period of the following function?

Find the input of the function corresponding to the output .

Find the input of the function corresponding to the output to three decimal places.

Use properties of limits and algebraic methods to find the limit, if it exists.

In 1990, there were 2 women among the CEOs of Fortune 500 companies. In 2009, this number had risen to 18 women. What was the percentage change in the number of Fortune 500 women CEOs between 1990 and 2009?

Indicate whether the function is an increasing or decreasing logistic function and identify the upper limiting value of the function

Use properties of limits and algebraic methods to find the limit, if it exists.

How long would it take an investment to double if the interest rate is 4.2%, compounded monthly? Round your answer to two decimal places.

Complete the table and use it to predict the limit, if it exists.

Indicate whether the function is an increasing or decreasing logistic function and identify the upper limiting value of the function .

Calculate the average rate of change in the population (in people per month) between April, 1999, and July, 2001.

The following table gives the percent of the U.S. population with Internet connections for the years 1997 to 2003. Use a calculator to find the logistic function that models these data. Use x as the number of years past 1995. Source: U.S. Department of Commerce

Use the formula to find the doubling time t, in years, for an investment at r% compounded n times per year. Suppose you make an investment of $1300 at interest rate 12% compounded quarterly. How long will it take for your investment to double?

Describing Change: Rates

Determining Change: Derivatives

Analyzing Change: Applications of Derivatives

Accumulating Change: Limits of Sums and the Definite Integral

Analyzing Accumulated Change: Integrals in Action

Ingredients of Multivariable Change: Models, Graphs, Rates

Analyzing Multivariable Change: Optimization

Filters