#### Problem 72E

72. After injection of a dose $D$ of insulin, the concentration of insulin in a patient’s system decays exponentially and so it can be written as $D e^{-a t}$, where $t$ represents time in hours and $a$ is a positive constant.

(a) If a dose $D$ is injected every $T$ hours, write an expression for the sum of the residual concentrations just before the $(n+1)$ st injection.

(b) Determine the limiting pre-injection concentration.

(c) If the concentration of insulin must always remain at or above a critical value $C$, determine a minimal dosage $D$ in terms of $C, a$, and $T$.