Q. The population of a village increases continuously at the rate proportional to the number of its inhabitants present at any time. If the population of the village was in and in the year , the population of the village in is

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Solution:

Let be the population at time , then
, where is constant

On integrating both sides, we get (i)
In the year
From equation (i),
(ii)
In the year , so from Eq. (i)

[using Eq. (iii)]



For year
Now, substituting the values of and in Eq. (i), we get




Hence, the population of the village in 2009 will be 31250 .