Chapter 4.4, Problem 52ES

The concentration $C\left(t\right)$ of a drug in the bloodstream $t$ hours after it has been injected is commonly modeled by an equation of the form $C\left(t\right)=\frac{K\left(e^{-bt}-e^{-qt}\right)}{a-b}$ where $K>0$ and $a>b>0$ .

(a) At what time does the maximum concentration occur?

(b) Let $K=1$ for simplicity, and use a graphing utility to check your result in part (a) by graphing $C\left(t\right)$ for various values of $a$ and $b$ .