Calculus (d) Estimate, to two significant figures, the average rate of change of

Question

Calculus

(d) Estimate, to two significant figures, the average rate of change of government funding for the arts over the period [0, 8]. (Be careful to state the units of measurement.)

_____ (thousand dollars per year, dollars per year, billion dollars per year, million dollars per year)

The following chart shows the total annual support for the arts in a country by federal, state, and local government in 1995-2003 as a function of time in years (t = 0 represents 1995) together with the regression line. (Assume a = 1.25, b 1.65, and c = 2.05.) Government funding for the Arts 4 1995 2003 Year (t) (a) Over the period [0, 4] the average rate of change of government funding for the arts was less than the rate predicted by the regression line greater than the rate predicted by the regression line approximately equal to the rate predicted by the regression line. (b) Over the period [4, 8] the average rate of change of government funding for the arts was less than the rate predicted by the regression line greater than the rate predicted by the regression line. approximately equal to the rate predicted by the regression line. (c) Over the period [3, 6] the average rate of change of government funding for the arts was less than the rate predicted by the regression line greater than the rate predicted by the regression line. approximately equal to the rate predicted by the regression line.

Explanation / Answer

d) the average rate of change in [0,8] is given by [ f(8) - f(0) ]/[8-0]

f(8) = (a+b)/2 = (1.25+1.65)/2 = 2.9/2 = 1.45

f(0) = b = 1.65

hence rate of change = (1.45-1.65)/8 =- 0.2/8 = -0.025 $ Billion per year

is negative so obiviously its less than slope of regretion

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