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) = 3 + t; D(t) = 9 − t; k = 0.01; p₀ = 1