exponential function

exponential function
1. the function y = ex.
2. any function of the form y = bax, where a and b are positive constants.
3. any function in which a variable appears as an exponent and may also appear as a base, as y = x2x.

* * *

In mathematics, a function in which a constant base is raised to a variable power.

Exponential functions are used to model changes in population size, in the spread of diseases, and in the growth of investments. They can also accurately predict types of decline typified by radioactive decay (see half-life). The essence of exponential growth, and a characteristic of all exponential growth functions, is that they double in size over regular intervals. The most important exponential function is ex, the inverse of the natural logarithmic function (see logarithm).

* * *

 in mathematics, a relation of the form y = ax, with the independent variable x ranging over the entire real number line as the exponent of a positive number a. Probably the most important of the exponential functions is y = ex, sometimes written y = exp (x), in which e (2.7182818…) is the base of the natural system of logarithms (logarithm) (ln). By definition x is a logarithm, and there is thus a logarithmic function that is the inverse of the exponential function (see figure—>). Specifically, if y = ex, then x = ln y. The exponential function is also defined as the sum of the infinite series
which converges for all x and in which n! is a product of the first n positive integers. Thus in particular, the constant

      The exponential functions are examples of nonalgebraic, or transcendental, functions—i.e., functions that cannot be represented as the product, sum, and difference of variables raised to some nonnegative integer power. Other common transcendental functions are the logarithmic functions and the trigonometric functions. Exponential functions frequently arise and quantitatively describe a number of phenomena in physics, such as radioactive decay (analysis), in which the rate of change in a process or substance depends directly on its current value.

* * *

Universalium. 2010.

Игры ⚽ Поможем написать реферат

Look at other dictionaries:

  • Exponential function — The natural exponential function y = ex In mathematics, the exponential function is the function ex, where e is the number (approximately 2.718281828) such that the function ex is its own derivative …   Wikipedia

  • exponential function — eksponentinė funkcija statusas T sritis fizika atitikmenys: angl. exponential function vok. exponentielle Funktion, f rus. экспоненциальная функция, f pranc. fonction exponentielle, f …   Fizikos terminų žodynas

  • exponential function — noun a function in which an independent variable appears as an exponent (Freq. 1) • Syn: ↑exponential • Derivationally related forms: ↑exponential (for: ↑exponential) • Hypernyms: ↑ …   Useful english dictionary

  • exponential function — noun Date: 1879 a mathematical function in which an independent variable appears in one of the exponents called also exponential …   New Collegiate Dictionary

  • exponential function — noun Mathematics a function whose value is a constant raised to the power of the argument, especially the function where the constant is e …   English new terms dictionary

  • exponential function — noun Any function in which an independent variable is in the form of an exponent; they are the inverse functions of logarithms …   Wiktionary

  • Stretched exponential function — Figure 1. Illustration of a stretched exponential fit (with β=0.52) to an empirical master curve. For comparison, a least squares single and a double exponential fit are also shown. The data are rotational anisotropy of anthracene in… …   Wikipedia

  • Double exponential function — A double exponential function (red curve) compared to a single exponential function (blue curve). A double exponential function is a constant raised to the power of an exponential function. The general formula is , which grows much more quickly… …   Wikipedia

  • Ultra exponential function — Articleissues OR=January 2008 other=This article uses nonstandard notations, which are confusing and superfluous.In mathematics the ultra exponential function is a special case of the iterated exponential function more commonly known as tetration …   Wikipedia

  • p-adic exponential function — In mathematics, particularly p adic analysis, the p adic exponential function is a p adic analogue of the usual exponential function on the complex numbers. As in the complex case, it has an inverse function named the p adic logarithm. Contents 1 …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”