Chapter 4.4, Problem 95E

Revenue Growth The demand for the Cyberpunk II arcade video game is modeled by the logistic curve

$q\left(t\right)=\frac{10,000}{1+0.5e^{-0.4t}},$

where $q\left(t\right)$ is the total number of units sold t months after its introduction.

a. Use technology to estimate $q\text{'}\left(4\right)$.

b. Assume that the manufacturers of Cyberpunk II sell each unit for $\$800$. What is the company’s marginal revenue $dR/dq$?

c. Use the chain rule to estimate the rate at which revenue is growing 4 months after the introduction of the video game.