Bounded growth, also called
asymptotic growth,
occurs when the growth rate of a mathematical function is constantly increasing at a decreasing rate. Asymptotically, bounded growth approaches a fixed value. This contrasts with
exponential growth
Exponential growth occurs when a quantity grows as an exponential function of time. The quantity grows at a rate directly proportional to its present size. For example, when it is 3 times as big as it is now, it will be growing 3 times as fast ...
, which is constantly increasing at an accelerating rate, and therefore approaches infinity in the limit.
Examples of bounded growth include the
logistic function
A logistic function or logistic curve is a common S-shaped curve ( sigmoid curve) with the equation
f(x) = \frac
where
The logistic function has domain the real numbers, the limit as x \to -\infty is 0, and the limit as x \to +\infty is L.
...
, the
Gompertz function, and a simple modified
exponential function like y = a + be
gx.
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]
See also
* Exponential growth
Exponential growth occurs when a quantity grows as an exponential function of time. The quantity grows at a rate directly proportional to its present size. For example, when it is 3 times as big as it is now, it will be growing 3 times as fast ...
* Gompertz function
* Logistic function
A logistic function or logistic curve is a common S-shaped curve ( sigmoid curve) with the equation
f(x) = \frac
where
The logistic function has domain the real numbers, the limit as x \to -\infty is 0, and the limit as x \to +\infty is L.
...
References
Sources
* Kuhn, Moscibroda, and Wattenhofer, "On the Locality of Bounded Growth", ACM Symposium on Principles of Distributed Computing (PODC), July 17–20, 2005.
* Gilchrist, Warren, "Statistical Modelling", John Wiley & Sons, Chichester, UK, 1984.
Mathematical modeling
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