Brine is flowing into a tank containing 50 lb of salt dissolved in 300 gallons of water. The salt concentration of the brine is 2 lb/gal, the input rate is 3 gal/min. The well-stired mixture is draining from the tank at a rate of 3 gal/min. Let *A(t)* be the amount of salt in the tank (in lb) at time *t*.

- Find an initial value problem for
*A*and solve it. - What happens as time goes to infinity?
- If the output rate is only 2 gal/min, find the corresponding initial value problem.