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 e^{r 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 e^{r t}

In other words find t if

2 = e^{r 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.

Penny

Go to Math Central