It is applied to population growth, inflation, resource extraction, consumption of goods, compound interest, the volume of malignant tumours, and many other things that tend to grow over time.
[2] The notion of doubling time dates to interest on loans in Babylonian mathematics.
Clay tablets from circa 2000 BCE include the exercise "Given an interest rate of 1/60 per month (no compounding), come the doubling time."
[3][4] Further, repaying double the initial amount of a loan, after a fixed time, was common commercial practice of the period: a common Assyrian loan of 1900 BCE consisted of loaning 2 minas of gold, getting back 4 in five years,[3] and an Egyptian proverb of the time was "If wealth is placed where it bears interest, it comes back to you redoubled.
For a constant growth rate of r % within time t, the formula for the doubling time Td is given by A common rule-of-thumb can be derived by Taylor series expanding the denominator ln(1+x) for x=0 using
Some doubling times calculated with this formula are shown in this table.
When applied to the constant growth in consumption of a resource, the total amount consumed in one doubling period equals the total amount consumed in all previous periods.
This enabled U.S. President Jimmy Carter to note in a speech in 1977 that in each of the previous two decades the world had used more oil than in all of previous history (The roughly exponential growth in world oil consumption between 1950 and 1970 had a doubling period of under a decade).