The rates of change in population for two cities are P'(t) = 42 for Alphaville and Q'(t) = 1020.05t 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 5000, 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) = 42t + 5000 . The population model for Betaburgh is Q(t) = 2040e0.05t + 960 . b) What were the populations of Alphaville and Betaburgh, to the nearest hundred, in 2000? The population of Alphaville in 2000 was people. (Round to the nearest hundred as needed.)