A tank originally contains 100 liters of water with a concentration of 50 g/l. Water containing 200 g/l is poured into the tank at a rate of 2 l/min and the mixture from the tank is allowed to flow out at the same rate. After 10 minutes the process is stopped, and fresh water is poured into the tank at a rate of 4 l/min with the mixture again leaving the tank at the same rate. Please show all work. No work = no credit.
a) Formulate a differential equation and initial values for the first 10 minutes.
b) Do the same for the second 10 minutes. Find a formula for the amount of salt in the tank for 10 ≤ t ≤ 20.
c) Find the amount of salt in the tank at the end of an additional 10 min.