Question

A country's population in 1994 was 195 million. In 2002 it was 199 million. How do you estimate the population in 2016 using the exponential growth formula?

Answer 1

Population in 2016 is estimated to be `206.20` million

Explanation:

Let the population in starting year be `P_0` and `g` be the exponential growth. Then the population `P_n` in `n^th` will be given by `P_n=P_0xx(1+g)^n`.

As the population in 1994 was 195 million and in 2002 (after 8 years), it was 199 million. We have

`199=195xx(1+g)^8` or `(1+g)^8=199/195`.

Taking log, `8xxlog(1+g)=log199-log195=0.0088185` or

`log(1+g)=0.0011022` or `1+g=1.002541` or `g=0.002541` i.e.

Growth rate is `0.2541%`.

The population in 2016 (after 22 years) would be

`195xx(1+g)^22` or `195xx1.002541^22=195xx1.0574279=206.20` million.