This exercise uses the population growth model.

The population of a certain city was128,000in 2014, and the observed doubling time for the population is19years.

(a) Find an exponential modeln(t) =n₀2^t/a

for the populationtyears after 2014.

n(t) =128000(2)t

19

(b) Find an exponential modeln(t) =n₀e^rt

for the populationtyears after 2014. (Round yourrvalue to four decimal places.)

n(t) =128000e0.046

(c) Sketch a graph of the population at timet.

(d) Estimate how long it takes the population to reach 500,000. (Round your answer to two decimal places.