Objective 2.11 and 2.13

A product is introduced to the market. The weekly profit in thousands of dollars of that product decays exponentially as function of the price that is charged (in dollars) and is given by $\displaystyle {M}{\left({p}\right)}={85}\cdot{e}^{{-{0.04}\cdot{p}}}$

And suppose the price in dollars of that product, $\displaystyle {p}{\left({t}\right)}$, is a function of time $\displaystyle {t}$ in weeks and is given by $\displaystyle {p}{\left({t}\right)}={51}+{0.85}\cdot{t}^{{2}}$

Find the marginal(ROC of) profit as a function of time, $\displaystyle {M}'{\left({t}\right)}$ Preview Question 6 Part 1 of 3  
hint: chain rule,

What is the the marginal (Rate of Change of) profit with respect to time 7 weeks after the introduction. hint: it is possible to do this in your calculator without the previous answer

Interpret your answer
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