Question

If the population of a country doubles in 60 years; in how many years will it be triple (treble) under the assumption that the rate of increase is proportional to the number of inhabitants?

[Given log 2 = 0.6912, log 3 = 1.0986]

Answer 1

Let P be the population at time t years. 

Then dP/dt, the rate of increase of population is proportional to P.

On integrating, we get

Since, the population doubles in 60 years, i.e. when t = 60, P = 2P₀

When population becomes triple, i.e. when p = 3p₀, we get

∴ the population becomes triple in 95.4 years (approximately).

Answer 2

Approximately 95.4 Years