Question $11,2\mathrm{.}2\mathrm{.}47-$BE

HW Score: $96\mathrm{.}67\%,11\mathrm{.}6$ of $12$ points

Part $1$ of $5$

Points: $0\mathrm{.}6$ of $1$

A company's total cost, in millions of dollars, is given by $C(t)=90=40e^{-t}$ where $t$ is the time in years since the start$-$up date. The graph of $C(t)$ is shown to the right. Find each of the following.

a$)$ The marginal cost, $C^{\text{'}}(t)$

b$)C^{\text{'}}(0)$

c$)C^{\text{'}}(6)$

d$)$ Find $\underset{t}{lim}C(t)$ and $\underset{t}{lim}{C}^{\text{'}}(t).$

a$)C^{\text{'}}(t)=($Do not include the $ symbol in your answer.$)$