A company finds that the rate at which the quantity of a product that consumers demand changes with respect to price is given by the marginal-demand function 4000 D'(X) = - x 2 where x is the price per unit, in dollars. Find the demand function if it is known that 1005 units of the product are demanded by consumers when the price is $4 per unit. D(X) =The rates of change in population for two cities are P'(t) = 42 for Alphaville and Q'(t) = 102 e 0.06t for Betaburgh, where t is the number of years since 1990, and P' and Q' are measured in people per year. In 1990, Alphaville had a population of 6000, and Betaburgh had a population of 3000. Answer parts a) through c). a) Determine the population models for both cities. The population model for Alphaville is P(t) =9 Find f such that f' (x) = f(1) = 27. VX f (x ) =