Exponential growth
growth of quantities at rate proportional to the current amount
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 as it is now.
In more technical language, its instantaneous rate of change (that is, the derivative) of a quantity with respect to an independent variable is proportional to the quantity itself. Often the independent variable is time. Described as a function, a quantity undergoing exponential growth is an exponential function of time, that is, the variable representing time is the exponent (in contrast to other types of growth, such as quadratic growth). Exponential growth is the inverse of logarithmic growth.
Terms like "exponential growth" are sometimes incorrectly interpreted as "rapid growth." Indeed, something that grows exponentially can in fact be growing slowly at first. Also, not all cases of growth at an always increasing rate are instances of exponential growth. For example the function
f
(
x
)
=
x
3
{\textstyle f(x)=x^{3}}
grows at an ever increasing rate, but is much slower than growing exponentially.
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This entry incorporates text from “Exponential growth” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.