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Question 1

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 2

Sales of Gigantic State University Rugby Team memorabilia at the GSU bookstore for the months January-April were given by the following table:

 Month Jan. (t=0) Feb. (t=1) Mar. (t=2) Apr. (t=3) Sales (\$) 200 300 450 675

Which model is more appropriate: a linear model s(t) = mt + b or an exponential model s(t) = abt? Use your choice of models to predict sales in May.

Question 3

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 about 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 4

Match the following functions with their graphs.

(1) f(x) = |x| (2) g(x) = 1/x2 (3) h(x) = x + 1/x2 (4) r(x) = x21

Question 5

The two fraternities Sigma Mu and Epsilon Alpha plan to raise money in a joint effort to benefit homeless people on Long Island. They will sell Jurassic Park T shirts in the student center, but are not sure how much to charge. Sigma Mu treasurer Solo recalls that they once sold 400 shirts in a week at \$8 each, while Epsilon Alpha treasurer Justino claims that, based on past experience, they can sell 600 per week if they charge \$5 each.

(a) Based on the above anecdotal information, construct a linear demand equation for Jurassic Park T shirts, giving weekly sales q as a linear function of unit price p?

(b) At what price should Sigma Mu and Epsilon Alpha sell the T shirts in order to obtain the largest possible revenue?

(c) Approximately how many T shirts would they sell at that price?

Question 6

In airline industry terminology, one A.S.M. represents one passanger seat (whether sold or vacant) flown one mile. The following table shows Kiwi Airlines' growing capacity, measured in millions of A.S.M.s per month, for the period from February, 1994 through February, 1995.*

 Time Feb. 1994 (t = 0) Nov. 1994 (t = 0.75) Feb. 1995 (t = 1) Capacity(Million ASMs) 110 155 174.9

(a) Fit the data for February, 1994 and February, 1995 to an exponential model of the form

C(t) = Abt

for suitable constants A and b.

(b) How accurately does your model predict the November, 1994 figure?

(c) When, to the nearest quarter-year, does your model predict Kiwi's capacity as 400 A.S.M.s per month?

* The figures are rounded. Source: Company Reports/The New York Times, March 25, 1995, p. D5.