Thread: How to derive the rule of 70 from the basic mathematics of exponential growth?

Hello, everyone! When I studyed demograph, I came across the rule of 70 which is a quich way to calculate the time it takes for a population growing at a specified rate to double its size. But I don't know how the formula derived from the basic mathematics of exponential growth. Can anyone tell me? Many thanks.

It's explained here.
EcoFuture™ Population and Sustainability - Exponential Growth and The Rule of 70

The Rule of 70 is useful for financial as well as demographic analysis. It states that to find the doubling time of a quantity growing at a given annual percentage rate, divide the percentage number into 70 to obtain the approximate number of years required to double. For example, at a 10% annual growth rate, doubling time is 70 / 10 = 7 years.

A special case is the doubling time, which is the time when N(t)/N(0) = 2, that is the quantity has doubled from its initial value. At that point

rt = ln 2 = 0.69

Thanks, you help me a lot.