Chapter 3.2, Problem 8E

A tank initially contains $S_0\text{lb}$ of salt dissolved in 200 gal of water, where $S_0$ is some positive number. Starting at time $t=0$, water containing $0.5\text{lb}$ of salt per gallon enters the tank at a rate of $4\text{gal/min}$, and the well – stirred solution leaves the tank at the same rate. Letting $c\left(t\right)$ be the concentration of salt in the tank at time $t$, show that the limiting concentration – that is ${\lim }_{\to \infty }c\left(t\right)$ is $0.5\text{lb/gal}$.