At t = 0, a tank of volume 300 liters is filled with 100 L of water containing salt at a concentration of 8 g/L. Fresh water flows in at a rate of 40 L/min, mixes instantaneously, and exits at the same rate. Let c₁(t) be the salt concentration at time t.
(a) Find a differential equation satisfied by c₁(t) Find the differential equation for the quantity of salt y(t), and observe that c₁(t) = y(t)/100.
(b) Find the salt concentration c₁(t) in the tank as a function of time.