Chapter 1.1, Problem 14P

A certain drug is being administered intravenously to a hospital patient. Fluid containing $5{\text{mg/cm}}^{\text{3}}$ of the drug enters the patient’s bloodstream at a rate of $100{\text{cm}}^{\text{3}}\text{/h}$. The drug is absorbed by body tissues or otherwise leaves the bloodstream at a rate proportional to the amount present, with a $0.4{\text{h}}^{\text{-1}}$.

Assuming that the drug is always uniformly distributedthroughout the bloodstream, write a differential equation for the amount of the drug that is present in the bloodstream atany time.

How much of the drug is present in the bloodstream aftera long time?