Objective 2.9

A product is introduced into the market.

Suppose a product's sales quantity per month q(t)\displaystyle {q}{\left({t}\right)} is a function of time t\displaystyle {t} in months is given by q(t)=5000t160t2\displaystyle {q}{\left({t}\right)}={5000}{t}-{160}{t}^{{2}}

And suppose the price in dollars of that product, p(t)\displaystyle {p}{\left({t}\right)}, is also a function of time t\displaystyle {t} in months and is given by p(t)=160t2\displaystyle {p}{\left({t}\right)}={160}-{t}^{{2}}

A. Find, R(t)\displaystyle {R}'{\left({t}\right)}, the rate of change of revenue as a function of time t\displaystyle {t}
 
expanding and collected not required

B. What is the the rate of change of revenue with respect to time 4 months after the introduction.


C. Interpret your answer in part B include the units of the number in part B