Deck 1: Ingredients of Change: Functions an Limits

Question 1

For the function, write the equations for any horizontal asymptote(s).

A) and
B) and
C)
D)
E) no horizontal asymptotes

Answer 1

and

Question 2

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

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

Answer 2

does not exist

Question 3

Numerically estimate the limits. Show the numerical estimation table. start , increment estimate to the nearest integer.

A)
B)
C)
D)
E)

Answer 3

Question 4

Write a linear model for the given rate of change and initial output value. The cost to produce plastic toys increases by 10 cents per toy produced. The fixed cost is 90 dollars.

A)
B)
C)
D)
E)

Question 5

Calculate the output value that corresponds to the given input values of the function.

A)
B)
C)
D)
E)

Question 6

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

A)
B)
C)
D)
E)

Question 7

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

A) -1
B) 14
C) -14
D) 1
E) does not exist

Question 8

Given evaluate Round to the nearest ten-thousandth.

A) 426.75
B) 400.429
C) 406.429
D) 2.9975

Question 9

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

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

Question 10

Evaluate the function at the given values of the independent variables.

A)
B)
C)
D)
E)

Question 11

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

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

Question 12

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

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 13

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

A)
B)
C)
D)
E)

Question 14

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.

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

Question 15

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

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

Question 16

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.

A)
B)
C)
D)
E)

Question 17

Find the input of the function corresponding to the output .

A)
B)
C)
D)
E)

Question 18

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

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

Question 19

Calculate the constant percentage change for the given function.

A) 15%
B) 0.15%
C) 72%
D) 82.8%
E) 10.8%

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?

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

Question 21

In 1996, the population of a country was estimated at 4 million. For any subsequent year the population in millions is where t is the number of years since 1996. Use a graphing calculator to estimate the population in 2005.

A) 4,743,000
B) 4,699,000
C) 4,655,000
D) 4,833,000

Question 22

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

A)
B)
C)
D)
E)

Question 23

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

A) The function is decreasing and the upper limit is 29.00.
B) The function is decreasing and the upper limit is 2.37.
C) The function is decreasing and the upper limit is -2.37.
D) The function is increasing and the upper limit is 0.00.
E) The function is increasing and the upper limit is 29.00.

Question 24

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?

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

Question 25

Your credit card statement indicates a finance charge of 20.00 % per month on the outstanding balance. What is the effective rate of interest (APY) to the nearest hundredth?

A) 20.00 %
B) 21.94 %
C) 21.67 %
D) 240.00 %
E) 1.67 %

Question 26

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%.

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 27

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

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 28

Choose the function type for the mathematical model that best represents the given data set.

A) logistic
B) quadratic
C) linear
D) exponential
E) logarithmic

Question 29

Calculate the total amount due after two years on a loan of $1100 with a simple interest charge of 7%.

A) $1254
B) $1204
C) $1304
D) $1354
E) $1154

Question 30

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?

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

Question 31

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

A)
B)
C)
D)
E)

Question 32

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

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 33

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.

A)
B)
C)
D)
E)

Question 34

Find the equation of the quadratic function that is the best fit for the given data.

A)
B)
C)
D)
E)

Question 35

A chemical reaction begins when a certain mixture reaches C. The reaction activity is measured in units (U) per 100 microliters of the mixture. Measurements during the first 18 minutes after the mixture reaches C are listed in the accompanying table. Estimate the limiting value.

A) 3.86
B) 1.93
C) 4.06
D) 3.83
E) 1.73

Question 36

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

A)
B)
C)
D)
E)

Question 37

Write the product of the two functions. Evaluate the constructed function at 2.

A)
B)
C)
D)
E)

Question 38

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.

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

Question 39

What is the period of the following function?

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

Question 40

It cost a company $6.75 to produce 75 glass bottles. What was the average cost of production of a glass bottle to the nearest cent?

A) $0.07
B) $0.75
C) $0.14
D) $40.88
E) $0.09

Question 41

The table below gives the normal daily mean temperatures, based on a 30-year period 1961 through 1990, for a certain city. Use the data to estimate the period.

A) 11 months
B) 2 months
C) 4 months
D) 12 months
E) 360 months

Question 42

Find the amplitude of the following function. Round to two decimal places.

A) 5.00
B) 2.00
C) 1.26
D) 3.14
E) 4.00

Question 43

What is the amplitude of the following function?

A) 5
B) 7
C) 10
D) 1
E) -1

Question 44

Find the period of the following function. Round to two decimal places.

A) 1.00
B) 6.28
C) 4.00
D) 1.57
E) 8.00

Question 45

What is the horizontal shift of the following function?

A) right
B) left 8
C) right 3
D) left
E) left 3

Question 46

Some populations of animals exhibit periodic behavior over time. During the 1960s and 1970s, two scientists carefully studied the population of the Carabid beetle in a region of the Netherlands. Assume that the table below shows the results from their study. Renumber the input data as years since 1965. Using only the data, estimate the horizontal shift, where a shift of zero corresponds to the year 1964. Round your answer to the nearest year.

A) 4 years
B) 34 years
C) 7 years
D) 5 years
E) 3 years

Question 47

Find the amplitude of the following function. Round to two decimal places.

A) 3.00
B) 8.00
C) 5.00
D) 0.00
E) 2.00

Question 48

The table below gives the normal daily mean temperatures, based on a 30-year period 1961 through 1990, for a certain city. Which of the following sine models best represents the mean daily temperature, where x denotes the number of the month in a calendar year.

A)
B)
C)
D)
E)

Question 49

Some populations of animals exhibit periodic behavior over time. During the 1960s and 1970s, two scientists carefully studied the population of the Carabid beetle in a region of the Netherlands. Assume that the table below shows the results from their study. Without the aid of technology, choose the sine model which is the most reasonable fit to data, where x is the number of years since 1964.

A)
B)
C)
D)
E)

Question 50

The table below gives the normal daily mean temperatures, based on a 30-year period 1961 through 1990, for a certain city. Use the data to estimate the amplitude to the nearest degree.

A)
B)
C)
D)
E)