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Question

In the 2001 census, the population of India was found to be 8.7×107. If the population increases at the rate of 2.5% every year, what would be population in 2011? The population of India in 2011 is k×107, then what is k?

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Solution

Here, P0=8.7×107, r=2.5, and n=10
Let P be the population in 2011. Then,
P=P0(1+r100)n
=8.7×107(1+2.5100)10
=8.7×107(1.025)10
Taking log on both side, we get
logP=log[8.7×107(1.025)10]
=log8.7+log107+log(1.025)10
=log8.7+7log10+10log(1.025)
=0.9395+7+0.1070
=8.0465
P=antilog(8.0465)=1.113×108 (using antilog table)
To compare with given population , writing it in that form 11.13×107
So, k=11.13

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