Question

The population of a place increased to \(54000\) in \(2003\) at a rate of \(5\) % per annum 

1. find the population in \(2001\) 
2. what would be its population in \(2005\)?

Answer 1

(i) It is given that, population in the year \(2003\) = \(54,000\)
Therefore,
\(54000\) = \((Population\; in \;2001)\) \(\bigg(1 + \frac{5}{100}\bigg)^2\)

\(Population \;in \;2001\) = \(54000 × \frac{20}{21} × \frac{20}{21}\) = \(48979.59\)

Thus, the population in the year \(2001\) was approximately \(48,980\).

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(ii) \(Population\; in\; 2005\) = \(54000\bigg(1+\frac{5}{100}\bigg)^2\)

\(54000\bigg(1+\frac{1}{20}\bigg)^2 = 54000 × \frac{21}{20} × \frac{21}{20} = 59,535\)

Thus, the population in the year \(2005\) would be \(59,535\).