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Question
The population of a suburb is 16000. Find the rate of increase in the population if the population after two years is 17640.
Solution
Here, P = Population of a suburb = 16000
A = Population after two years =17640
R = R %
N = 2 years
A = P `(1 + "R"/100)^"N"`
= 17640 = 16000 `(1 + "R"/100)^2`
= `17640/16000` = `(1 + "R"/100)^2`
= `441/400` = `(1 + "R"/100)^2`
Taking square roots from both
= `(1 + "R"/100) = _-^+(21/20)`
= `"R"/100` = `21/20`
= `"R"/100 = _-^+ 21/20 - 1`
= `"R" /100 (+ 21/20-1) or (-21/20-1)`
= `"R"/100(1/20) or (-41/20)`
= `"R" = (1/20 xx 100) or (-41/20 xx 100)`
= R = 5 or R = −205
Hence, the rate of increase in the population is 5 p.c.p.a.
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