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For any fixed b not equal to 1 (e.g. e or 2), the growth rate is given by the non-zero time τ. For any non-zero time τ the growth rate is given by the dimensionless positive number b. Thus the law of exponential growth can be written in different but mathematically equivalent forms, by using a different base.
The graph on the right is an exponential growth projection made in July 2006. The number of articles on the English Wikipedia up to July 2006 is shown in red, and this is extrapolated in blue using an exponential function (approximately 38000*exp(0.0017 t ) articles, where t is the number of days since January 1, 2001).
A finite group has constant growth—that is, polynomial growth of order 0—and this includes fundamental groups of manifolds whose universal cover is compact. If M is a closed negatively curved Riemannian manifold then its fundamental group has exponential growth rate.
r = the population growth rate, which Ronald Fisher called the Malthusian parameter of population growth in The Genetical Theory of Natural Selection, [2] and Alfred J. Lotka called the intrinsic rate of increase, [3] [4] t = time. The model can also be written in the form of a differential equation: =
Exponential growth or exponential decay—where the varaible change is proportional to the variable ... rate constant, [8] or ... It shows the graph is a surface of ...
Relative growth rate (RGR) is growth rate relative to size - that is, a rate of growth per unit time, as a proportion of its size at that moment in time. It is also called the exponential growth rate, or the continuous growth rate.
As resources become more limited, the growth rate tapers off, and eventually, once growth rates are at the carrying capacity of the environment, the population size will taper off. [6] This S-shaped curve observed in logistic growth is a more accurate model than exponential growth for observing real-life population growth of organisms. [8]
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.