Question 5 (20% or 30 minutes) Consider the model of price adjustment with inventory. The demand is: 9a = 500 - 3p 9s = 100 + 2p And the price adjustment equation is: p = 0.05(9d - 43) - 0.5(qs - 9d) a) Write the differential equation for price. b) Find the general solution. c) Assume that p(0) = 50 and p(0) = 20, find the solution of the differential equation. d) Now, suppose that the demand is continuously shifting as t increases. The demand is now: qa = (500 + 0.5t) - 3p Find the solution to the differential equation