For Exercise, the models f represent per capita consumption of food items. Per capita is a...

For Exercise, the models f represent per capita consumption of food items. Per capita is a Latin phrase meaning “for each person.” The population of the United States can be modeled by various functions, but for these exercises, we will use the linear model

 g(x) = 2.85x + 224.36 0 ≤ x ≤ 31

where x represents the number of years since 1980, and g(x) represents the U.S. population from 1980 to 2011 in millions of people. (Source: U.S. Census Bureau.)

Nutrition—Orange Consumption: Many people who have adjusted their diets to eat more fresh fruit have been challenged with steadily increasing prices for fresh fruit. “Orange juice fortified with calcium may help fortify bones and fight osteoporosis, and the vitamin C naturally found in oranges may inhibit cancer,” said Deepak Chopra, MD. (Source: The Chopra Center.) The per capita consumption of oranges in the United States from 1980 to 2011 can be modeled by

 f(x) = −0.18x + 14.43 0 ≤ x ≤ 31

where x represents the number of years since 1980, and f(x) represents the per capita consumption of oranges, measured in pounds per person annually. (Source: U.S. Department of Agriculture.)

(a) Examine the coefficient of x in the model f. Interpret the meaning of this value.

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(b) Simplify the product of functions (f · g). What does this function represent?

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(c) Evaluate (f · g) (28), and interpret the product. Keep in mind the units for the function g.