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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.
The standard logistic function is the logistic function with parameters =, =, =, which yields = + = + = / / + /.In practice, due to the nature of the exponential function, it is often sufficient to compute the standard logistic function for over a small range of real numbers, such as a range contained in [−6, +6], as it quickly converges very close to its saturation values of 0 and 1.
Thus, the equation relates the growth rate of the population N to the current population size, incorporating the effect of the two constant parameters r and K. (Note that decrease is negative growth.) The choice of the letter K came from the German Kapazitätsgrenze (capacity limit), while r came from rate.
Moreover, the function makes use of initial growth rate, which is commonly seen in populations of bacterial and cancer cells, which undergo the log phase and grow rapidly in numbers. Despite its popularity, the function initial rate of tumor growth is difficult to predetermine given the varying microcosms present with a patient, or varying ...
On a log–linear plot (logarithmic scale on the y-axis), pick some fixed point (x 0, F 0), where F 0 is shorthand for F(x 0), somewhere on the straight line in the above graph, and further some other arbitrary point (x 1, F 1) on the same graph.
The effect is that the population growth rate is again very low, because either each individual is hardly reproducing or mortality rates are high. [13] As a result of these two extremes, the population growth rate is maximum at an intermediate population or half the carrying capacity (=).
Sub-exponential growth [ edit ] A common explanation for the growth of epidemics holds that 1 person infects 2, those 2 infect 4 and so on and so on with the number of infected doubling every generation.
In microbiology, the rapidly growing exponential growth phase of a cell culture is sometimes called logarithmic growth. During this bacterial growth phase, the number of new cells appearing is proportional to the population. This terminological confusion between logarithmic growth and exponential growth may be explained by the fact that ...