The population P (in thousands) of Tallahassee, Florida, from 2000 through 2014 can be modeled by P = 150.9ekt, where t represents the year, with t = 0 corresponding to 2000. In 2005, the population of Tallahassee was about 163,075.
(a) Find the value of k. Is the population increasing or decreasing? Explain.
(b) Use the model to predict the populations of Tallahassee in 2020 and 2025. Are the results reasonable? Explain.
(c) According to the model, during what year will the population reach 200,000?