Doubling time

The doubling time (also called doubling time or double value time) describes the period of time in which an exponentially growing quantity (for example the population of a country) doubles. It enables better comparability of the growth of different sizes compared to the comparison based on the absolute change in size. A smaller doubling time means faster growth, a larger doubling time means slower growth. The doubling time is related to the half-life . In microbiology it is also referred to as generation time .

definition

The doubling time is calculated from the growth rate or the growth factor using the following equation : ${\displaystyle p}$ ${\displaystyle q}$

${\displaystyle t_{V}={\frac {\ln(2)}{\ln(1+p)}}={\frac {\ln(2)}{\ln(q)}}}$

Example: If the population of a country grows by 2% annually, the growth factor is . This results in a doubling time of . So the population doubles about every 35 years. ${\displaystyle q=1{,}02}$ ${\displaystyle t_{V}={\tfrac {\ln(2)}{\ln(1{,}02)}}\approx 35{,}0028}$

An approximate calculation from the growth rate (given in percent) is e.g. As with the 70-rule possible . Example: With an annual population growth of 2%, the doubling time is about years. ${\displaystyle p}$ ${\displaystyle t_{V}\approx {\tfrac {70}{p}}}$ ${\displaystyle t_{V}\approx {\tfrac {70}{2}}=35}$

Individual evidence

1. ↑ Doubling time - Mathebibel.de. Retrieved April 4, 2020 .