Often sales of a new product grow rapidly at first and then level off with time.

Question

Often sales of a new product grow rapidly at first and then level off with time. This is the case with the sales represented by the function S(t) = 400 - 500t-1, where t represents time in years. Find the rate of change of sales for the following number of years. 2 years The rate of change in sales after 2 years is . (Type an integer or decimal rounded to the nearest thousandth as needed.) 6 years The rate of change in sales after 6 years is . (Type an integer or decimal rounded to the nearest thousandth as needed.)

Explanation / Answer

a) 2years d/dt( s(t)) = 500t^-2 sub t=2 d/dt ( s(t)) = 500/4 = 125 b) 6years d/dt ( s(t)) = 500/36= 13.88

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