In Exercises 63 through 66, the supply S(t) and demand D(t) functions for a commodity are given in terms of the unit price p(t) at time t. Assume that price changes at a rate proportional to the shortage D(t) – S(t), with the indicated constant of proportionality k and initial price p₀. In each exercise:

(a) Set up and solve a differential equation for p(t).

(b) Find the unit price of the commodity when t = 4.

(c) Determine what happens to the price as t → ∞?

S(t) = 2 + 3p(t); D(t) = 10 − p(t); k = 0.02; p₀ = 1