A storage tank initially contains 100 L of pure water
MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations
Problem
A storage tank initially contains 100 L of pure water. Beginning at time t=0 minutes, brine containing 0.10 kg of dissolved chemical per litre flows into the tank at 4 L/min, while the well-mixed solution flows out at 2 L/min.
Let M(t) be the mass of dissolved chemical (in kilograms) in the tank at time t minutes, and let V(t) be the volume of liquid (in litres) in the tank at that time.
(a) Express V(t) as a function of t and state its domain of validity.
(b) Derive a differential equation satisfied by M(t) for the time interval during which the tank is not full. Clearly indicate how V(t) enters into your model.
(c) Solve the differential equation from part (b) to obtain an explicit formula for M(t).
(d) Determine the concentration V(t)M(t) just as the tank reaches its capacity of 500 L, and compute the time at which this occurs.