Difference between revisions of "Exponential growth"
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The expression "exponential growth" is often used to mean "tremendous growth" because an exponential function with a [[basis]] greater than 1 grows faster than any [[polynomial function]]s. Formally, for any basis ''a''>1 there is a number ''n'' such that, for any ''x''>''n'', ''x'' to the power of ''n'' is strictly greater than ''x'' to the power of ''a''. Colloquially, for any pair of one exponential function and one polynomial function there is a point ''n'' at which the former, provided its exponent is large enough, will overtake the latter. | The expression "exponential growth" is often used to mean "tremendous growth" because an exponential function with a [[basis]] greater than 1 grows faster than any [[polynomial function]]s. Formally, for any basis ''a''>1 there is a number ''n'' such that, for any ''x''>''n'', ''x'' to the power of ''n'' is strictly greater than ''x'' to the power of ''a''. Colloquially, for any pair of one exponential function and one polynomial function there is a point ''n'' at which the former, provided its exponent is large enough, will overtake the latter. | ||
| + | ==See also== | ||
| + | *[[Exponential decay]] | ||
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Latest revision as of 15:11, December 14, 2009
Exponential growth is growth like an exponential function.
The expression "exponential growth" is often used to mean "tremendous growth" because an exponential function with a basis greater than 1 grows faster than any polynomial functions. Formally, for any basis a>1 there is a number n such that, for any x>n, x to the power of n is strictly greater than x to the power of a. Colloquially, for any pair of one exponential function and one polynomial function there is a point n at which the former, provided its exponent is large enough, will overtake the latter.