Question

The population of Knoxville is 500,000 and is increasing at the rate of 3.75% each year. Approximately when will the population reach 1 million? Use an exponential model to solve the problem.

Answer 1

dp/dt = .0375 people/year

ln p = .0375 t + c

p = c e^(.0375 t)
when t = 0, p = 500,000
so
p = 500,000 e^(.0375 t)

so
2 = 1,000,000/500,000 = e^(.0375 t)
ln 2 = .0375 t

t = 18.5 years