Chapter 3.1, Problem 2E

What is interpolation when using a linear model?

Sales Barnes & Noble had annual sales of $6.8 billion in 2013 and $6.1 billion in 2015. Use the Midpoint Formula to estimate the sales in 2014. Assume that the annual sales followed a linear pattern.

A soccer stadium holds 62,000 spectators. With aticket price of$11, the average attendance has been26,000. When the price dropped to $9, the averageattendance rose to 31,000. Assuming that attendanceis linearly related to ticket price, what ticket pricewould maximize revenue?

Redo Exercise 5, assuming that the house blend contains 300 grams of Colombian beans, 50 grams of Kenyan beans, and 150 grams of French roast beans and the gourmet blend contains 100 grams of Colombian beans, 350 grams of Kenyan beans, and 50 grams of French roast beans. This time the merchant has on hand 30 kilograms of Colombian beans, 15 kilograms of Kenyan beans, and 15 kilograms of French roast beans. Suppose one bag of the house blend produces a profit of $0.50, one bag of the special blend produces a profit of $1.50, and one bag of the gourmet blend produces a profit of $2.00. How many bags of each type should the merchant prepare if he wants to use up all of the beans and maximize his profit? What is the maximum profit?

LIFE SCIENCE APPLICATIONS HIV Infection The time interval between a persons initial infection with HIV and that persons eventual development of AIDS symptoms is an important issue. The method of infection with HIV affects the time interval before AIDS develops. One study of HIV patients who were infected by intravenous drug use found that 17 of the patients had AIDS after 4 years and 33 had developed the disease after 7 years. The relationship between the time interval and the percentage of patients with AIDS can be modeled accurately with a linear equation. Source: Epidemiologic Review. a. Write a linear equation y=mt+b that models these data, using the ordered pairs (4,0.17) and (7,0.33). b. Use your equation from part a to predict the number of years before half of these patients will have AIDS.