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?

Mar 7, 2016

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 ${n}^{t} h$ will be given by ${P}_{n} = {P}_{0} \times {\left(1 + g\right)}^{n}$.

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

$199 = 195 \times {\left(1 + g\right)}^{8}$ or ${\left(1 + g\right)}^{8} = \frac{199}{195}$.

Taking log, $8 \times \log \left(1 + g\right) = \log 199 - \log 195 = 0.0088185$ or

$\log \left(1 + g\right) = 0.0011022$ 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

$195 \times {\left(1 + g\right)}^{22}$ or $195 \times {1.002541}^{22} = 195 \times 1.0574279 = 206.20$ million.