Question

The population of a village is 20000. If the annual birth rate is $4\%$ and the annual death rate $2\%$, calculate the population after two years.

Answer 1

We have,

Annual birth rate $=4\%$, Annual death rate $=2\%$

$\therefore$ Annual growth $=(4-2)\%=2\%$

Thus, we have

P = Initial population = 20000, R = Rate of growth $=2\%$ per annum, n = 2 years

$\therefore$ Population after 2 years $=P{(1+\frac{R}{100})}^n$

$=20000\times {(1+\frac{2}{100})}^2$

$=20000\times {(1+\frac{1}{50})}^2$

$=20000\times {\left(\frac{51}{50}\right)}^2=20000\times \frac{51}{50}\times \frac{51}{50}=20808$

Hence, the population of the town after 2 years = 20808.