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Growth equations. Like exponential growth and logistic growth, hyperbolic growth is highly nonlinear, but differs in important respects.These functions can be confused, as exponential growth, hyperbolic growth, and the first half of logistic growth are convex functions; however their asymptotic behavior (behavior as input gets large) differs dramatically:
However, if some elements of {α} or {β} are not zero, then function S has multitudes of additional singularities and cutlines in the complex plane, due to the exponential growth of sin and cos along the imaginary axis; the smaller the coefficients {α} and {β} are, the further away these singularities are from the real axis.
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.
Geometric progressions show exponential growth or exponential decline, as opposed to arithmetic progressions showing linear growth or linear decline. This comparison was taken by T.R. Malthus as the mathematical foundation of his An Essay on the Principle of Population.
Exponential decay, decrease at a rate proportional to value; Exponential discounting, a specific form of the discount function, used in the analysis of choice over time; Exponential growth, where the growth rate of a mathematical function is proportional to the function's current value; Exponential map (Riemannian geometry), in Riemannian geometry
Exponential smoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function. Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time. It is an easily learned ...
Asymptotically, bounded growth approaches a fixed value. This contrasts with exponential growth, which is constantly increasing at an accelerating rate, and therefore approaches infinity in the limit. Examples of bounded growth include the logistic function, the Gompertz function, and a simple modified exponential function like y = a + be gx. [1]
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time ...