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?

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