The population of a city increases each year by 4% of what it had been

1.	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 (1) 2001 (ii) 1997.
Answer» Given, Annually increase rate of population of city = 4% Population in 1999 = 6760000 So , i) Population of city in 2001 (2 years after) \(= 6760000({1}+\frac{4}{100})({1}+\frac{4}{100})\) \(= 6760000\times\frac{26}{25}\times\frac{26}{25}\) = 7311616. ii) Population of city in 1997 (2 years ago) \(= 6760000({1}-\frac{4}{100})({1}-\frac{4}{100})\) \(= 6760000\times\frac{21}{25}\times\frac{21}{25}\) = 6750000

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 (1) 2001 (ii) 1997.

Answer»

Given,

Annually increase rate of population of city = 4%

Population in 1999 = 6760000

So ,

i) Population of city in 2001 (2 years after)

\(= 6760000({1}+\frac{4}{100})({1}+\frac{4}{100})\)

\(= 6760000\times\frac{26}{25}\times\frac{26}{25}\) = 7311616.

ii) Population of city in 1997 (2 years ago)

\(= 6760000({1}-\frac{4}{100})({1}-\frac{4}{100})\)

\(= 6760000\times\frac{21}{25}\times\frac{21}{25}\) = 6750000