Calculus Question

Question

The rate of growth, in dollars per year, of the net worth, f(t), of a company is given by f′(t)=2750−10t^2, where t is measured in years since 1989. How does the net worth of the company change between 1989 and 2000? 

Answer 1

Integrate 2750 - 10 t² to get f(t) = 2750 t - (10/3) t³ + C. Let t = 0 for year 1989 and f(0) = C. For year 2000, t = 11 and f(11) = 30,250 - 4436.67 + C. The change in net worth is f(11) - f(0) = $25,813.33.