Exponential series

Exponential series
Exponential Ex`po*nen"tial, a. [Cf. F. exponentiel.] 1. Pertaining to exponents; involving variable exponents; as, an exponential expression; exponential calculus; an exponential function. [1913 Webster]

2. changing over time in an exponential manner, i. e. increasing or decreasing by a fixed ratio for each unit of time; as, exponential growth; exponential decay. [PJC]

Note:

{Exponential growth} is characteristic of bacteria and other living populations in circumstances where the conditions of growth are favorable, and all required nutrients are plentiful. For example, the bacterium {Escherichia coli} in rich media may double in number every 20 minutes until one of the nutrients becomes exhausted or waste products begin to inhibit growth. Many fascinating thought experiments are proposed on the theme of exponential growth. One may calculate, for example how long it would take the progeny of one {Escherichia coli} to equal the mass of the known universe if it multiplied unimpeded at such a rate. The answer, assuming the equivalent of 10^{80} hydrogen atoms in the universe, is less than three days. Exponential increases in a quantity can be surprising, and this principle is often used by banks to make investment at a certain rate of interest seem to be very profitable over time.

{Exponential decay} is exhibited by decay of radioactive materials and some chemical reactions (first order reactions), in which one-half of the initial quantity of radioactive element (or chemical substance) is lost for each lapse of a characteristic time called the {half-life}. [PJC]

{Exponential curve}, a curve whose nature is defined by means of an exponential equation.

{Exponential equation}, an equation which contains an exponential quantity, or in which the unknown quantity enters as an exponent.

{Exponential quantity} (Math.), a quantity whose exponent is unknown or variable, as a^{x}.

{Exponential series}, a series derived from the development of exponential equations or quantities. [1913 Webster]


The Collaborative International Dictionary of English. 2000.

Игры ⚽ Нужен реферат?

Look at other dictionaries:

  • exponential series — noun a series derived from the expansion of an exponential expression • Hypernyms: ↑series * * * noun : a series derived from the development of exponential expressions; specifically : the fundamental expansion ex = 1 + x/1 + x²/2! + x³/3!+…,… …   Useful english dictionary

  • Exponential — Ex po*nen tial, a. [Cf. F. exponentiel.] 1. Pertaining to exponents; involving variable exponents; as, an exponential expression; exponential calculus; an exponential function. [1913 Webster] 2. changing over time in an exponential manner, i. e.… …   The Collaborative International Dictionary of English

  • Exponential curve — Exponential Ex po*nen tial, a. [Cf. F. exponentiel.] 1. Pertaining to exponents; involving variable exponents; as, an exponential expression; exponential calculus; an exponential function. [1913 Webster] 2. changing over time in an exponential… …   The Collaborative International Dictionary of English

  • Exponential decay — Exponential Ex po*nen tial, a. [Cf. F. exponentiel.] 1. Pertaining to exponents; involving variable exponents; as, an exponential expression; exponential calculus; an exponential function. [1913 Webster] 2. changing over time in an exponential… …   The Collaborative International Dictionary of English

  • Exponential equation — Exponential Ex po*nen tial, a. [Cf. F. exponentiel.] 1. Pertaining to exponents; involving variable exponents; as, an exponential expression; exponential calculus; an exponential function. [1913 Webster] 2. changing over time in an exponential… …   The Collaborative International Dictionary of English

  • Exponential growth — Exponential Ex po*nen tial, a. [Cf. F. exponentiel.] 1. Pertaining to exponents; involving variable exponents; as, an exponential expression; exponential calculus; an exponential function. [1913 Webster] 2. changing over time in an exponential… …   The Collaborative International Dictionary of English

  • Exponential quantity — Exponential Ex po*nen tial, a. [Cf. F. exponentiel.] 1. Pertaining to exponents; involving variable exponents; as, an exponential expression; exponential calculus; an exponential function. [1913 Webster] 2. changing over time in an exponential… …   The Collaborative International Dictionary of English

  • Exponential smoothing — is a technique that can be applied to time series data, either to produce smoothed data for presentation, or to make forecasts. The time series data themselves are a sequence of observations. The observed phenomenon may be an essentially random… …   Wikipedia

  • Exponential integral — is a mathematical function of a single argument which has no established notation.DefinitionsFor real values of x , the exponential integral Ei( x ) can be defined as : mbox{Ei}(x)=int { infty}^xfrac{e^t}t,dt., The definition above can be used… …   Wikipedia

  • exponential theorem — noun A theorem that gives a value of any number in terms of its natural logarithm, and from which can at once be derived a series determining the logarithm • • • Main Entry: ↑exponent …   Useful english dictionary

Share the article and excerpts

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