Rule of 70 to approximate population doubling time | AP Environmental Science | Khan Academy

When we're dealing with population growth rates, an interesting question is how long would it take for a given rate for the population to double. So we're going to think about doubling time now.

If you were to actually calculate it precisely, mathematically, it gets a little bit mathy. You need to use a little bit of logarithms and you'll probably need a calculator. But I did that here in the spreadsheet by calculating the exact doubling time.

So this is saying that if a population is growing at one percent a year, it's going to take almost 70 years for that population to double. But if that population is growing at 5 percent a year, then it's going to take a little over 14 years for that population to double. If the population is growing at 10 percent, we know mathematically it's going to take a little bit over seven years for that population to double.

Now, I was able to calculate this, as I just mentioned, using a little bit of fancy math. But what we see in this next column is there's actually a pretty easy way to approximate doubling time, and this is known as the rule of 70. The rule of 70 is used in a lot of different areas, a lot of different subjects. People in finance would use it because, once again, you're thinking about things growing at a certain percent every year. But you can also use it for things like population growth rates.

So what we see with the rule of 70—and let me just write that down, rule of 70—is that you can approximate the doubling time by taking the number 70 and dividing it by the—not actually the percentage but just the number of the percentage. So for example, this right over here is 70 divided by this one here, which is equal to 10.

And notice this 70 is pretty close to 69.7. If you wanted to figure out, or you wanted to approximate, the doubling time if the population is growing at 7 percent a year, well, what you would say is, all right, what is 70 divided by 7? Well, that is equal to 10. So this would be your approximation, and if you were doing it in a mathematically precise way, it would be 10.2.

So if you're taking, say, an AP Environmental Science course and they're asking you for how long it takes for something to double, let's say a population is growing 7 percent a year, they're probably expecting you to use the rule of 70.

So let's say that we have a population that is growing at 14 percent a year, and that would actually be a very huge growth rate. What I want you to do is pause this video and approximate how long would it take for that population to double.

All right, now let's work through this together. So as I mentioned, we're approximating; we don't have to calculate the exact doubling time. So for approximating it, it's going to be 70 divided by the rate of growth.

So in this situation, this is going to be 70 divided by 14, which is equal to 5. So if a population is going at 14 percent, it'll take it roughly 5 years to double.