Question

The population of the city was $20000$ in the year $1997$ it increases at the rate of $5\%$ per annum find the population at the end of the Year $2000.$

Answer 1

The population of the city in 1997 is 20000.

Then, Population, $P=20000$

Rate of increment, $R=5\%$

We have to find the population at the end of year $2000,$ i.e. Time, $n=3$ years

Population after $3$ years is given by

$P^{\prime }=P(1+\frac{R}{100}{)}^n$

$=20000(1+\frac{5}{100}{)}^3$

$=20000(\frac{105}{100}{)}^3$

$=20000\left(\frac{105}{100}\right)\times \left(\frac{105}{100}\right)\times \left(\frac{105}{100}\right)$

$=23152.5$

Hence, the population of the city at the end of $2000$ will be approx $23152$ people.