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Answer :
(i) We are given: Population in 2003 = 54,000, Rate = 5% p.a.
Time = 2003 – 2001 = 2 years
\(Population\; in \;2003 = Population\; in \;2001\times(1+\frac{R}{100})^n\)
\(\Rightarrow 54,000=Population\; of \;2001\times(1+\frac{5}{100})^2\)
\(\Rightarrow 54,000=Population \;of \;2001\times(\frac{21}{20})^2\)
\(\Rightarrow 54,000=Population\; of \;2001\times(\frac{441}{400})\)
∴ Population of 2001= \(\frac{54,000\times 400}{441}\)
= \(\frac{21,6,00,000}{441}=48,979.59≈48,980\)
(ii) \(Population \;in \;2005= Population\;in\;2003\times(1+\frac{R}{100})^n\)
\( =54,000\times(1+\frac{5}{100})^2\)
\( =54,000\times(\frac{21}{20})^2\)
\( =54,000\times(\frac{441}{400})^2\)
\(=135\times441=59,535\)