# 10 The population of a place increased to 54,000 in 2003 at a rate of 5% per annum                    (i) find the population in 2001.

Let the population in 2001 be P

Compound rate of increase = 5% p.a.

The population in 2003 will be more than in 2001

Time period, n = 2 years    (2001 to 2003)

$\therefore$ $\\ 54000 = P(1 + \frac{5}{100})^2 \\ \implies P = \frac{54000\times100\times100}{105\times105} \approx 48980$

Therefore, the population in 2001 was 48980 (approx)

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