compund interest

Question

In​ 2012, the population of the city was 6.19 million. The exponential growth rate was 2.73​% 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 8 ​million?

​d) Find the doubling time.

Answer 1

A= Pe^.0273t where P = population at time t=0, A = population at time t,

A=6.19e^.0273t where A is measured in millions, t= years since 2012

in 2018, t= 6

A=6.19e^.0273(6) = about 7.29 million in 2018

8/6.19 = e^.0273t

.0273t = ln(8/6.19)

t = [ln(8/6.19)]/.0273 = about 9.4 =2012+9.4= about 2021 or mid-2022

doubling time is when

2=e^.0273t

t=(ln2)/.0273= about 25.4 years

or 2012+25.4= about 2037 or mid 2038

when population reaches 2x6.19= 12.38 million