(e) Why does no linear function exactly fit the data?
Question 3 Let g be the function with the graph shown.
Question 5 Select a function to match each of the following graphs.
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.
(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.
(a) Which of the following functions best models the data?
(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.
(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 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?
(c) Approximately how many T-shirts would they sell at that price?
Question 12 Continuing Question 11, suppose that old Slayer CDs cost the Delta Nuttal store $2.00 each, with fixed costs of $1,000 per week for advertising.
(a) Use this data with that of Question 11 to give the weekly cost as a function of the unit price x they charge per CD.
(b) Use the results of part (a) and Question 11 to give the weekly profit in terms of the unit price x, and hence determine how much they should charge for maximum weekly profit.
(a) Use the data from 1977 and 1982 to model the math score m as a linear function of the science score s.
(b) Is your model consistent with the 1992 data?
(c) What does the slope in your model signify about science and math scores?
† Data are accurate to two significant digits, with the third digit "massaged" to simplify the calculation. Source: Department of Education's National Assessment of Educational Progress/The New York Times, August 18, 1994, p. A14.