Question

The population of a city increases each year by $4\%$ of what it had been at the beginning of each year. If the population in 1999 had been 6760000, find the population of the city in

(i) 2001

ii) 1997

Answer 1

Population of a city in 1999 = 6760000
Increase $=4\%$
(i) $\therefore$ Population in 2001 is after 2 years
$=6760000\times {(1+\frac{4}{100})}^2$
$=6760000\times {\left(\frac{26}{25}\right)}^2$
$=6760000\times \frac{26}{25}\times \frac{26}{25}=7311616$

(ii) Let population in 1997 = P
Then 6760000 $=P{(1+\frac{4}{100})}^2$
$=P\times {\left(\frac{26}{25}\right)}^2=P\times \frac{676}{625}$
$\therefore P=6760000\times \frac{625}{676}=6250000$
$\therefore$ Population in 1997 was = 6250000.