Question

The population of a city is 20,000. If the rate of increase is 25% every year, then find the population after 2 years. $\left[1\text{Mark}\right]$

Answer 1

$\text{Given:}$
$\text{Population,P}=20,000$
$\text{Rate of increase in population,}R=25\%\text{and}\text{Number of years, n}=2\text{years}$

$\text{Let population after 2 years be A.}$

$A=P\times {[1+\frac{R}{100}]}^n=20,000\times [1+\frac{25}{100}{]}^2=20,000\times [1+\frac{1}{4}{]}^2=20,000\times [\frac{5}{4}{]}^2=20,000\times \frac{25}{16}=31,250$

$\therefore \text{The population after 2 years}=31,250$