The product is introduced to market. Weekly profit (in dollars) of that product decays exponentially as function of price which is charged (in dollars) and is provided by P(x)=95000*e^(-0.02*x)
Assume price in dollars of that product, x(t), changes over time t (in weeks) as provided by x(t)=40+0.82*t^2
Determine rate that profit changes as the function of time, P'(t)?
How fast profit is changing with respect to time five weeks after introduction?