Chapter 2.3, Problem 5P

A tank contains $100\text{gal}$ of water and $50\text{oz}$ of salt. Water containing a salt concentration of $\frac{1}{4}\left(1+\frac{1}{2}\sin t\right)\text{oz}/\text{gal}$ flows into the tank at a rate of $2\text{gal}/\min$, and the mixture in the tank flows out at the same rate.

Find the amount of salt in the tank at any time.

Plot the solution for a time period long enough so that you see the ultimate behaviour of the graph.

The long-time behaviour of the solution is an oscillation about a certain constant level. What is this level? What is the amplitude of the oscillation?