Quandaries and Queries


Looking for the equation to how many years it will take to double the population given the growth rate is 7%. This is for a programming class I am taking. Not really interested in an answer, just the equation to solve the question.


Hi Nick,

The conventional way to approach this is to assume that the growth rate of the population is directly proportional to the size of the population. This leads to the expression

P(t) = P0 er t

where t is the time, P(t) is the population size at time t, P0 is the population size at time 0 and r is the growth rate. The doubling time is the time t when P(t) = 2 P0 . Thus you need to find t when

2 P0 = P0 er t

In other words find t if

2 = er t

If you take the natural log of both sides you have

ln(2) = r t

and hence

t = ln(2)/r

When r = 0.7 as in your question I get a doubling time of 9.9. The units are determined by the growth rate. You says 7% but you didn't give units.



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