Science:Math Exam Resources/Courses/MATH104/December 2010/Question 06/Statement

At a certain time, the stock of a company listed on the Vancouver Stock Exchange is selling for $0.25 a share. The controlling shareholders spread a (quickly dispelled) rumour that the company has discovered a cure for death. This causes a surge of demand for the stock. As a result, when $t\geq {0}$ the price of a share is P(t) dollars, where

$\displaystyle {}P(t)=0.25+30t{\textrm {e}}^{-t/5}.$

Here t is measured in days and t = 0 at the instant the rumour starts. At what time t is the price of the stock increasing most rapidly? Please justify that the answer you calculate actually gives the greatest rate of increase.