Chapter 6.2, Problem 9E

Reminder Round all answers to decimal places unless otherwise indicated.

Health Plan The managers of an employee health plan for a firm have studied the balance $B$, in millions of dollars, in the plan account as a function of $t$, the number of years since the plan was instituted. They have determined that the rate of change $\frac{dB}{dt}$ in the account balance is given by the formula

$\frac{dB}{dt}=10e^{0.1t}-12$.

$a.$ Use your calculator to make a graph of $\frac{dB}{dt}$ versus $t$ over the first 5 years of the plan.

$b.$ During what period is the account balance $B$ decreasing?

$c.$ At what time is the account balance $B$ at its minimum?