When analyzing the effects of differences in economic growth rates over time, it is generally the case that seemingly small differences in annual growth rates result in large differences in the size of economies (usually measured by Gross Domestic Product, or GDP) over long time horizons. Therefore, it's helpful to have a rule of thumb that helps us quickly put growth rates into perspective.
One intuitively appealing summary statistic used to understand economic growth is the number of years it will take for the size of an economy to double. Fortunately, economists have a simple approximation for this time period, namely that the number of years it takes for an economy (or any other quantity, for that matter) to double in size is equal to 70 divided by the growth rate, in percent. This is illustrated by the formula above, and economists refer to this concept as the "rule of 70."
Some sources refer to the "rule of 69" or the "rule of 72," but these are just subtle variations on the rule of 70 concept and merely replace the numerical parameter in the formula above. The different parameters simply reflect different degrees of numerical precision and different assumptions regarding the frequency of compounding. (Specifically, 69 is the most precise parameter for continuous compounding but 70 is an easier number to calculate with, and 72 is a more accurate parameter for less frequent compounding and modest growth rates.)