The population P (in thousands) of a certain city from 2000 through 2014 can be modeled by
P = 130.8e^kt,
where t represents the year, with
t = 0
corresponding to 2000. In 2006, the population of the city was about 161,050.
(a) Find the value of k. (Round your answer to four decimal places.)
k =
Is the population increasing or decreasing? Explain.
Because k is negative, the population is decreasing.
(b) Use the model to predict the populations of the city (in thousands) in 2020 and 2025. (Round your answers to three decimal places.)
2020
P = __________
thousand people
2025
P = ___________
thousand people
Are the results reasonable? Explain.
The populations are not reasonable. The population cannot continue to increase at the same rate it did from the year 2020 to 2025.
(c) According to the model, during what year will the population reach 230,000?