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—Ice Cream Consumption: One of Americans’ favorite treats is ice cream. The per capita consumption of ice cream in the United States from 1980 to 2011 can be modeled by

 f(x) = −0.11x + 17.44 0 ≤ x ≤ 31

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

(a) Evaluatef(28) and g(28), and interpret each value.

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

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