Question

The population of a village declines by $5\%$ every year.If the present population of the village is $1444$, find the population of the village $2$ year back.

Answer 1

Given:-

Present population, $P=1444$,
Rate $=5\%$ and Time $=2$ years

Let the population of the village $2$ years back be $P_o.$

Now,

$P=P_o{(1-\frac{R}{100})}^n$
$\Rightarrow 1444=P_o{(1-\frac{5}{100})}^2$

$\Rightarrow 1444=P_o{\left(\frac{95}{100}\right)}^2$
$\Rightarrow P_o=\frac{1444\times 100\times 100}{95\times 95}$
$\Rightarrow P_o=1600$

Hence, the population of the village $2$ years back is equal to $1600.$