 ## Review Exercises for Applied Calculus Finite Mathematics & Applied Calculus Topic: Functions and Linear Models

Chapter 1 Summary
True/False Quiz
Index of Review Exercises
Everything for Calculus
Everything for Finite Math
Everything for Finite Math & Calculus
Utilities: Function Evaluator & Grapher | Excel Grapher | On-Line Regression Utilty | All Utilities Question 1 Let f be the function specified by the following table.

 x -2 -1 0 1 2 f(x) 5 2 1 2 5

 (a) f(1) = (b) f(1 - 2) = (c) f(1)-f(2) =
 (d) What kind of model best fits the data? Select one linear quadratic exponential logistic
 (e) Why does no linear function exactly fit the data?
 (f) The linear function which passes through the points where x = 0 and 2 is: (Note Use proper input syntax: e.g., use "3*x" instead of "3x".) g(x) =

 Question 2 Given f(x) = x - 1 x , find the following. (Note Use proper input syntax: e.g., use "3*x" instead of "3x".)

 (a) f(1) = (b) f(-1) = (c) f(x+h) = (d) f(x)+h = (e) f(x)+x =

Question 3 Let g be the function with the graph shown. g(-1) = g(2) - g(-1) 3 = -g(1) g(-1) = Question 4 Find linear functions for the following straight lines. (Note Use proper input syntax: e.g., use "3*x" instead of "3x".)
 (a) Through the origin with slope 3 y = (b) Through the point (1,-1) with slope 3 y = (c) Through the points (-3, -6) and (1, -1) y = (d) Through the point (1, -2) and parallel to the line x + 3y = 1 y = (e) Through the point (1, -1) and parallel to the line 2x - 3y = 11 y =

Question 5 Select a function to match each of the following graphs. Select one f(x) = -|x| f(x) = |x| - 1 f(x) = 1/x f(x) = 1/x^2 f(x) = x + 1/x^2 f(x) = x^2 - 1 f(x) = |x| + 2x^2 f(x) = 1 - x^2 f(x) = x + 1/x Select one f(x) = -|x| f(x) = |x| - 1 f(x) = 1/x f(x) = 1/x^2 f(x) = x + 1/x^2 f(x) = x^2 - 1 f(x) = |x| + 2x^2 f(x) = 1 - x^2 f(x) = x + 1/x Select one f(x) = -|x| f(x) = |x| - 1 f(x) = 1/x f(x) = 1/x^2 f(x) = x + 1/x^2 f(x) = x^2 - 1 f(x) = |x| + 2x^2 f(x) = 1 - x^2 f(x) = x + 1/x Select one f(x) = -|x| f(x) = |x| - 1 f(x) = 1/x f(x) = 1/x^2 f(x) = x + 1/x^2 f(x) = x^2 - 1 f(x) = |x| + 2x^2 f(x) = 1 - x^2 f(x) = x + 1/x

Question 6
US imports of pasta increased from 290 million pounds in 1990 (t = 0) by an average of 52 million pounds per year.* Use this to express annual US imports of pasta q (in millions of pounds) as a linear function of the number of years t since 1990, and use your model to predict US past imports in the year 2000.

* Data are rounded, and are for the period 1990 through 1994. Source: Department of Commerce/The New York Times, September 5, 1995, p. D4.

Question 7 The number C(t) of coffee shops and related enterprises in the US can be approximated by the following function of time t in years since 1990.*

 C(t)  = 500t + 800 if 0 t 4 1,300t - 2,400 if 4 < t 10

(a) Evaluate C(0), C(4) and C(5), and interpret the results.

(b) How fast was the number of coffee shops in the US growing in 1992 and in 1995?

(c) Use the model to estimate when there were 5,400 coffee shops in the US.

* Source for data: Specialty Coffee Association of America / The New York Times, August 13, 1995, p. F 10.

Question 8 The 50-member rugby team is planning to buy new gear for their next road trip to California. They are told by the suppliers that, if they order x game shirts, the cost per shirt is given by the following data:

 x (Number of shirts) 5 25 40 100 125 A(x)(Cost per shirt \$) 25.05 21.25 21.025 21.25 21.45

(a) Which of the following functions best models the data?

 0.005x + 20.75
 0.01x + 20
 0.01x + 20 - 25/x 0.01x + 20 + 25/x
 0.0005x2 - 0.07x + 23.25

(b) Graph A(x) in the window 10 x 100, 20 y 23 and use your graph to estimate the lowest cost per shirt, and the number of shirts they should buy to obtain the lowest price per shirt.

Question 9 The following table shows the average daily circulation of all the newspapers of two major newspaper companies.

 Number of Newspapers 82 26 Daily Circulation (Millions) 5.8 3

† Circulation figures are rounded to the nearest 0.1 million, and reflect average daily circulation as of September 30, 1994. Source: Newspaper Association of America/The New York Times, Juy 30, 1995, p. E6

(a) Use these data to express a company's daily circulation, c, as a linear function of the number, n, of newspapers it publishes.

(b) What information does the slope give to newspaper publishers?

(c) Your company plans to add 11 newspapers to its current 10. According to your model, how would this effect daily circulation?

Question 10 Carbon Emissions in the US increased more-or-less linearly from 1200 million metric tons in 1983 to 1500 million metric tons in 1999.* Use these figures to construct a linear model of US Carbon emissions C (in millions of metric tons) as a function of time t in years since 1980 (so that t = 0 represents 1980).

Enter your model here, using valid proper formula-entry syntax. Also, don't forget to use the correct letter for the independent variable.

 C(t) = *Data are rounded. Source: Natural Resources Defence Council/US Department of Energy/New York Times, June 15, 2001, p. A8.

Question 11 The TEP fraternity at Enormous State U is raising money to buy a Greek letter from the Phi Epsilon sorority (so that they can be known as the TEEPs) by selling back issues of the ESU Inquirer. The result of some sales data yielded the following demand equation

q = -8000p + 480
where p is the price they charge (in \$) for each copy, and q is the total sales. Select the correct statement.
 The fraternity can sell 8,000 more copies if they raise the price \$1. The fraternity can sell 8000 copies if they charge \$1 per copy. The fraternity will sell 480 fewer copies if they raise the price \$1. The fraternity can sell 8000 more copies if they lower the price \$1. None of the above.  