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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." This yields an annual interest rate of 12/60 = 20%, and hence a doubling time of 100% growth/20% growth per year = 5 years.
The doubling time (t d) of a population is the time required for the population to grow to twice its size. [24] We can calculate the doubling time of a geometric population using the equation: N t = λ t N 0 by exploiting our knowledge of the fact that the population (N) is twice its size (2N) after the doubling time. [20]
Most commonly apparent in species that reproduce quickly and asexually, like bacteria, exponential growth is intuitive from the fact that each organism can divide and produce two copies of itself. Each descendent bacterium can itself divide, again doubling the population size (as displayed in the above graph). [2]
The number of new bacteria appearing per unit time is proportional to the present population. If growth is not limited, doubling will continue at a constant rate so both the number of cells and the rate of population increase doubles with each consecutive time period.
A popular approximated method for calculating the doubling time from the growth rate is the rule of 70, that is, /. Graphs comparing doubling times and half lives of exponential growths (bold lines) and decay (faint lines), and their 70/ t and 72/ t approximations.
One may then define the generation time as the time it takes for the population to increase by a factor of . For example, in microbiology , a population of cells undergoing exponential growth by mitosis replaces each cell by two daughter cells, so that R 0 = 2 {\displaystyle \textstyle R_{0}=2} and T {\displaystyle T} is the population doubling ...
= size at time two When calculating or discussing relative growth rate, it is important to pay attention to the units of time being considered. [2] For example, if an initial population of S 0 bacteria doubles every twenty minutes, then at time interval it is given by solving the equation:
Population biology is especially concerned with the Gompertz function. This function is especially useful in describing the rapid growth of a certain population of organisms while also being able to account for the eventual horizontal asymptote, once the carrying capacity is determined (plateau cell/population number). It is modeled as follows: