Initially, a large tank with a capacity of 100 gallons contains 50 gallons of pure water. A salt solution with concentration of 0.1 lb/gal flows into the tank at a rate of 2 gal/min. The mixture is well stirred and flows out of the tank at the rate of 4 gal/min. Find the initial-value problem that describes the amount of salt in the tank until the tank is empty.