You haven't said what the TIME PERIOD is during which these rates are observed.
Still, I feel like working on this one, so I'm going to assume that these birth and death rates refer to a period of ONE YEAR, and now I'll proceed to answer the question that I have invented.
If there are 10 births and 8 deaths per 1,000 EACH YEAR, then the population grows by exactly 2 per 1,000 people per year. That's a growth rate of 0.2% per year.
In 1 year, the population grows by (1.002). In ' X ' years, the population grows by a factor of (1.002)ˣ .
We want to know what ' x ' has to be in order for (1.002)ˣ = 2 .
Take the log of each side: x log(1.002) = log(2)
Divide each side by log(1.002) : x = log(2) / log(1.002)
x = (0.30103) / (0.0008677)
x = 346.92
Doubling time = 346.92 years
(At the end of 346 years, the population hasn't doubled yet, but they don't quite have to wait another full year. Mathematically it'll only be another 0.92 year = ~336 days.)
