Question

The population of a city is 125000. If the annual birth rate and death rate are 5.5% and 3.5% respectively, calculate the population of city after 3 years.

Answer 1

$$\begin{gathered} \mathrm{Here}, \\ \mathrm{P}=\mathrm{Initial}\mathrm{population}=125,000 \\ \mathrm{Annual}\mathrm{birth}\mathrm{rate}={\mathrm{R}}_1=5.5\% \\ \mathrm{Annual}\mathrm{death}\mathrm{rate}={\mathrm{R}}_2=3.5\% \\ \mathrm{Net}\mathrm{growth}\mathrm{rate},\mathrm{R}=\left({\mathrm{R}}_1-{\mathrm{R}}_2\right)=2\% \\ \mathrm{n}=\mathrm{Number}\mathrm{of}\mathrm{years}=3 \\ \therefore \mathrm{Population}\mathrm{after}\mathrm{three}\mathrm{years}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{n}} \\ =125,000{\left(1+\frac{2}{100}\right)}^3 \\ =125,000{\left(1.02\right)}^3 \\ =132,651 \\ \mathrm{Hence},\mathrm{the}\mathrm{population}\mathrm{after}\mathrm{three}\mathrm{years}\mathrm{will}\mathrm{be}132,651. \end{gathered}$$