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

MATH104 December 2010
Other MATH104 Exams

### Question 06

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 ${\displaystyle t\geq {0}}$ the price of a share is P(t) dollars, where

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

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.

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