Chapter 2.2, Problem 87E

Drug Concentration When a pharmaceutical drug is injected into the bloodstream, its concentration at time $t$ can be approximated by $C\left(t\right)=C_o{e}^{-kt}$, where $C_o$ is the concentration at $t=0$. Suppose the drug is ineffective below a concentration $C_1$ and harmful above a concentration $C_2$. Then it can be shown that the drug should be given at intervals of time $T$, where

$T=\frac{1}{k}\ln \frac{C_2}{C_1}$

Source: Applications of Calculus to Medicine.

A certain drug is harmful at a concentration five times the concentration below which it is ineffective. At noon an injection of the drug results in a concentration of $2$ mg per liter of blood. Three hours later the concentration is down to $1$ mg per liter. How often should the drug be given?