Macroeconomics—Corporate Tax Rates: In a July 22, 2010, Associated Press interview, Treasu...

Macroeconomics—Corporate Tax Rates: In a July 22, 2010, Associated Press interview, Treasury Secretary Tim Geithner said, “We are likely to have to take a broader look at corporate tax reform next year,” adding that it was likely to be one of the areas the fiscal commission appointed by President Obama would examine to make recommendations on deficit reduction. The amount collected in U.S. corporate taxes annually from 1990 to 2010 can be modeled by

 f(x) = 1.65x + 13.13 0 ≤ x ≤ 20

where x represents the number of years since 1990 and f(x) represents the amount of corporate taxes collected in billions of dollars. The amount in corporate profits of U.S. corporations from 1990 to 2010 can be modeled by

 g(x) = 2.45x2 + 26.52x + 419.01 0 ≤ x ≤ 20

where x represents the number of years since 1990 and g(x) represents the corporate profits in billions of dollars. (Sources: Associated Press, U.S. Bureau of Economic Analysis.)

(a) Form the function to determine the ratio of taxes per profit as a percentage. Then graph h in the viewing window [0, 20] by [0, 4].

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(b) Determine h′(x).

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(c) Evaluate h′(3) and h′(18) and interpret each.