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The doubling time is the time it takes for a population to double in size/value. 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.
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. For this type of exponential growth, plotting the natural logarithm of cell number against time produces a straight line.
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]
The growth constant k is the frequency (number of times per unit time) of growing by a factor e; in finance it is also called the logarithmic return, continuously compounded return, or force of interest. The e-folding time τ is the time it takes to grow by a factor e. The doubling time T is the time it takes to double.
The formula above can be used for more than calculating the doubling time. If one wants to know the tripling time, for example, replace the constant 2 in the numerator with 3. As another example, if one wants to know the number of periods it takes for the initial value to rise by 50%, replace the constant 2 with 1.5.
One equation used to analyze biological exponential growth uses the birth and death rates in a population. If, in a hypothetical population of size N, the birth rates (per capita) are represented as b and death rates (per capita) as d, then the increase or decrease in N during a time period t will be = ()
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 ...
Therefore, the doubling time t d becomes a function of dilution rate D in steady state: t d = ln 2 D {\displaystyle t_{d}={\frac {\ln 2}{D}}} Each microorganism growing on a particular substrate has a maximal specific growth rate μ max (the rate of growth observed if growth is limited by internal constraints rather than external nutrients).