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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
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.
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Solution
\[(i)\]
Population of the city in 2001 = P \[\left( 1 + \frac{R}{100} \right)^2 \]
\[ = 6760000 \left( 1 + \frac{4}{100} \right)^2 \]
\[ = 6760000 \left( 1 . 04 \right)^2 \]
\[ = 7311616\]
Thus, Population of the city in 2001 is 7311616.
\[(ii)\]
Population of the city in 1997 = P \[\left( 1 + \frac{R}{100} \right)^{- 2} \]
\[ = 6760000 \left( 1 + \frac{4}{100} \right)^{- 2} \]
\[ = 6760000 \left( 1 . 04 \right)^{- 2} \]
\[ = 6250000\]
Thus, Population of the city in 1997 is 6250000.
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