A product is introduced to the market. The weekly profit (in dollars) of that product decays exponentially as function of the price that is charged (in dollars) and is given by $P(x) = 65000 \cdot e^{-0.05x}$
Suppose the price in dollars of that product, $x(t)$, changes over time $t$ (in weeks) as given by $x(t) = 39 + 0.76 \cdot t^2$
Find the rate that profit changes as a function of time, $P'(t)$ dollars/week
How fast is profit changing with respect to time 6 weeks after the introduction. dollars/week