Q1. An experimental mixing tank originally contains 100 gal of fresh water. A solution containing 1/2

pounds/gallon of salt is poured into the tank at a constant rate of 2 gal/min, and the mixture is

allowed to drain from the tank at the same rate. After 10 minutes have elapsed, this process is stopped

and the inflow is immediately switched to another solution containing fresh water that pours into the

tank at 2 gal/min, with the mixture in the tank continuing to drain at the same rate.

(a) Assuming that the tank is always well-mixed, write a pair of ODE initial value problems that

describe the time variation of the amount of salt Q(t) (in pounds) contained in the tank at any

time t (in minutes). Solve these IVPs to obtain an explicit representation for Q(t).

(b) Determine the amount of salt remaining in the tank 10 mins after the "switching time" (that is,

a total of 20 mins after the start of the experiment).

(c) Plot your solution Q(t) over the time interval 0 < t < 30 mins, taking care to clearly illustrate

what happens at time t = 10 mins.

(d) What happens to the amount of salt in the tank as t→ ∞? Explain.