Chapter 4.2, Problem 96E

Forecasting Profits As a result of increasing energy costs, the growth rate of the profit of the 4-year old Venice Glassblowing Company has begun to decline. Venice’s management, after consulting with energy experts, decides to implement certain energy-conservation measures aimed at cutting energy bills. The general manager reports that, according to his calculations, the growth rate of Venice’s profit should be on the increase again within 4 years. If Venice’s profit (in hundreds of dollars) t years from now is given by the function

P(t) = t³ – 9t² + 40t + 50 (0 ≤ t ≤ 8)

determine whether the general manager’s forecast will be accurate.