Question

The population of a city was 20,000 in the year 1997. It increased at the rate of 5% p.a. Find the population at the end of the year 2000.

Answer 1

There is 5% increase in population every year, so every new year has new population.

Population in the beginning of 1998 = 20000
Increase at 5% = ${\displaystyle \frac{5}{100}}$ × 20000 = 1000
Population in 1999 = 20000 + 1000 = 21000

Increase at 5% = ${\displaystyle \frac{5}{100}}$ × 21000 = 1050
Population in 2000 = 21000 + 1050 = 22050

Increase at 5% = ${\displaystyle \frac{5}{100}}$ × 22050 = 1102.5
At the end of 2000 the population = 22050 + 1102.5 = 23152.5

Answer 2

Population at the end of 2000 = 20000 ${\displaystyle {(1+\frac{5}{100})}^3}$
${\displaystyle =20000\times \frac{21}{20}\times \frac{21}{20}\times \frac{21}{20}}$
= 23152.5
So, the estimated population = 23153.