Objective 2.9

A product is introduced into the market.

Suppose a product's sales quantity per month $\displaystyle {q}{\left({t}\right)}$ is a function of time $\displaystyle {t}$ in months is given by $\displaystyle {q}{\left({t}\right)}={1000}{t}-{110}{t}^{{2}}$

And suppose the price in dollars of that product, $\displaystyle {p}{\left({t}\right)}$, is also a function of time $\displaystyle {t}$ in months and is given by $\displaystyle {p}{\left({t}\right)}={110}-{t}^{{2}}$

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

B. What is the the rate of change of revenue with respect to time 3 months after the introduction.


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