Math, Pre-calculus

Question

In​ 2012, the population of a city was 5.27 million. The exponential growth rate was 1.95% per year.

​a) Find the exponential growth function.

​b) Estimate the population of the city in 2018.

​c) When will the population of the city be

77

​million?

​d) Find the doubling time.

Answer 1

A=5.27e^.0198t where A is in millions, t=time since 2012

in 2018, t= 6

and

A= 5.27e^.0198(6) =about 5.93 million

77.00 =5.27e^.0198t

77/5.27 = e^.0198t

t = (ln(77/5.27)/.0198 = about 135

t+2012 = 2147 = year it reaches 77 million

2 = e^.0198t where t= doubling time

t = ln(2)/.0198 = about 35 years