Question

The population of a city is $20,000.$ Find the population of the city after three years if the population increase by $5\%$ every year .

Answer 1

Population after three years will be given by the formula ,

$A=P{\left(1+\frac{r}{100}\right)}^n$

Where $A=$Population of the city after three years

$P$= Current population of the city

$r=$rate of increase of population per year

$n=$Time period

Given , $P=20,000,r=5\%,n=3years.$

Substituting the given values in the formula we get ,

$$\begin{gathered} A=20,000{\left(1+\frac{5}{100}\right)}^3 \\ =20,000{\left(1+\frac{1}{20}\right)}^3 \\ =20,000{\left(\frac{21}{20}\right)}^3 \\ =20,000\times \frac{21}{20}\times \frac{21}{20}\times \frac{21}{20} \\ =23152.5 \end{gathered}$$

Hence the estimated population is $231523$

Hence the population of a city after three years is $231523.$