Question

The population of Andhra Pradesh $5.4\times {10}^7$ in $1988$. If the population was growing at a constant rate of $2.4\%$ p.a, what will be the population in $2008$?

Answer 1

The population of a particular year is given by

$\Rightarrow P_n=P_0{(1+\frac{r}{100})}^n$

where $P_0=$ Population in $1988=5.4\times {10}^7$

$P_n=$ Population in $n$ years after $1988$

$r=$ Population growth rate $=2.4\%$

$n=$ Number of years after $1988=20$

$\Rightarrow P_{2008}=5.4\times {10}^7{(1+\frac{2.4}{100})}^{20}$

$=5.4\times {10}^7\times 1.60694$

$=8.677\times {10}^7.$

Hence, the population in $2008$ will be $8.677\times {10}^7.$