# How do I calculate the annual growth rate of a population?

Okay, I’ve obviously forgotten all my post-Algebra II math, or I wouldn’t be asking the question. Here’s the problem:

A given population has increased from 30 million to 500 million over the span of 70 years. What is the annual growth rate of that population?

Anybody? I’m more interested in the appropriate method than the answer–i.e., show your work, and feel free to leave out the answer if you wish.

Thanks,
Rhymer

Okay, here’s what I’ve got so far.

The total growth rate of the 70-year period is 50/3, or something like 16.66667 fold increase. That’s easy enough.

For the average annual rate, though, you need some number that, multiplied by itself 70 times, is 16.66667 - that is, the 70th root of 16.66667, or 16.66667 to the power of (1/70)

you’ll need a scientific calculator to work that out I think My scientific calculator gives a growth rate of a bit more than .041 or 4.1 percent.

You don’t really need the calculator if you have a logarithm table and know how to use it.

(1 + R)^70 = 50 / 3
70 * log (1 + R) = log 50 - log 3
log (1 + R) = (log 50- log 3) / 70
1+ R = antilog [(log 50 - log 3) / 70]
R = antilog [(log 50 - log 3) / 70] - 1

Alternately, the answer can be worked out quickly on any calculator that handles exponents: [(50/3)^(1/70)]-1.