The population of a city increases each year by 4% of what it had been at the beginning of each year.

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.

Solution:

(i)

Population of the city in $2001=P\left(1+\frac{R}{100}\right)^{2}$

$=6760000\left(1+\frac{4}{100}\right)^{2}$

$=6760000(1.04)^{2}$

$=7311616$

Thus, Population of the city in 2001 is 7311616 .

(ii)

Population of the city in $1997=P\left(1+\frac{R}{100}\right)^{-2}$

$=6760000\left(1+\frac{4}{100}\right)^{-2}$

$=6760000(1.04)^{-2}$

$=6250000$

Thus, Population of the city in 1997 is 6250000 .

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