All courses › Mathematics S1 › Doubling time

Doubling time

The doubling time is how many periods it takes before a quantity has doubled, when the growth factor stays fixed. You set the growth factor raised to the time equal to 2, and solve with a logarithm. The time is the natural logarithm of 2, divided by the natural logarithm of the growth factor. A higher interest rate gives a shorter doubling time. The formula assumes that the percentage is the same in every period.

bt=2b^t = 2doubling
t=ln⁡2ln⁡bt = \frac{\ln 2}{\ln b}doubling time

Symbols

bbgrowth factor per period
ttnumber of periods

Example

At 5% interest the growth factor is 1.05.

t=ln⁡2ln⁡1.05≈14.21t = \dfrac{\ln 2}{\ln 1.05} \approx 14.21 years.

Use the growth factor, not the percentage, in the denominator.
Practise logarithms and exponential equations for free →

← Change of base · Growth by a fixed percentage →

Part of Mathematics S1: Logarithms and exponential equations.