Population Doubling Time
Time for a population to double.
Formula
Variables
Example
r=0.02 ⇒ 34.7 yr
How it works
This formula gives the time it takes for a quantity that is growing exponentially to become twice as large. It comes from the exponential growth model N(t)=N_0e^{rt}: to find the doubling time, set N(t)=2N_0 and solve 2=e^{rt}, which gives t=\ln 2 / r. It only applies when the growth rate r is constant and the population is increasing continuously rather than in fixed jumps.
When to use it
Use this when modeling populations, cell cultures, or any biological system that grows approximately exponentially with a known per-unit-time growth rate. It is especially useful for estimating how long bacteria, tumor cells, or wildlife populations take to double under steady conditions.
Worked example, step by step
A bacterial culture grows continuously at r = 0.08 per hour. Use the doubling-time formula: t_d = \ln 2 / r Substitute the value: t_d = 0.6931 / 0.08 Calculate: t_d = 8.664 hours Final answer: the population doubles in about 8.7 hours.
Common mistakes to avoid
- Using a percentage growth rate without converting it to a decimal rate per time unit
- Putting the growth rate in the denominator as 2/r instead of ln(2)/r
- Applying the formula to populations with limited resources or changing growth rates, where exponential growth is not a good model
Did You Know?
The rule of 70 estimates doubling time, so a 2% growth rate doubles a population in about 35 years.
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