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 5400 people. (Round to the nearest hundred as needed.) The population of Betaburgh in 2000 was 4300 people. (Round to the nearest hundred as needed.) c) Sketch the graph of each city's population model and estimate the year in which the two cities have the same population. Choose the correct graph below. O A. OB. OC. D. A Population (1,000s) 10- Q APopulation (1,000s) 10- A Population (1,000s) 10- A Population (1,000s) 10- Q 25 25 The two cities have the same population in the year (Round to the nearest year as needed.)