Exercises 43 and 44 provide some simple examples of an
Chapter 5, Problem 43(choose chapter or problem)
Exercises 43 and 44 provide some simple examples of an important idea that was presented in the chapter introduction: Exponential growth eventually outpaces polynomial growth (no matter how high the degree of the polynomial). In each case, carry out the calculations needed to verify the given statementLet f(x) 1.125x2 0.75x 1 and g(x) 2x.(a) On the interval [0, 2], both functions have the sameaverage rate of change. This is also true for the interval[2, 4].(b) On the interval [4, 6], however, g/x is more thantwice f/x. And on the interval [6, 8], g/x is morethan six times f/x.(c) On the interval [10, 12], the average rate of change ofthe exponential function is 64 times that of the quadraticfunction.4
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