Question

The population of a town is 125000. It is increasing at the rate of 2% per annum. What will be its population after 3 years?

Answer 1

$$\begin{gathered} \mathrm{Population}\mathrm{of}\mathrm{the}\mathrm{town},P=125000 \\ \mathrm{Rate}\mathrm{of}\mathrm{increase},\mathit{}R=2\% \\ \mathrm{Time},\mathit{}n=3\mathrm{years} \\ \mathrm{Then}\mathrm{the}\mathrm{population}\mathrm{of}\mathrm{the}\mathrm{town}\mathrm{after}3\mathrm{years}\mathrm{is}givenby \\ \mathrm{Population}=\mathit{}P\times {\left(1+\frac{R}{100}\right)}^3 \\ =125000\times {\left(1+\frac{2}{100}\right)}^3 \\ =125000\times {\left(\frac{100+2}{100}\right)}^3 \\ =125000\times {\left(\frac{102}{100}\right)}^3 \\ =125000\times {\left(\frac{51}{50}\right)}^3 \\ =125000\times \left(\frac{51}{50}\right)\times \left(\frac{51}{50}\right)\times \left(\frac{51}{50}\right) \\ =\left(51\times 51\times 51\right) \\ =132651 \\ \mathrm{Therefore},\mathrm{the}\mathrm{population}\mathrm{of}\mathrm{the}\mathrm{town}\mathrm{after}\mathrm{three}\mathrm{years}\mathrm{is}132651. \end{gathered}$$