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.