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