# Exponential growth

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 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.

### Look at other dictionaries:

• exponential growth — noun A stage of growth occurring in populations of unicellular micro organisms when the logarithm of the cell number increases linearly with time • • • Main Entry: ↑exponent …   Useful english dictionary

• exponential growth —  Exponential Growth  Рост по показательному закону   Рост или воспроизводство с удвоением количества в течение заданного периода времени. Часто ошибочно называется «самовоспроизводством» …   Толковый англо-русский словарь по нанотехнологии. - М.

• Exponential growth — The graph illustrates how exponential growth (green) surpasses both linear (red) and cubic (blue) growth.   Exponential growth …   Wikipedia

• Exponential Growth — A pattern of increasing prices that resembles the curve of an exponential function. In finance, exponential growth is caused by compounding returns. Given enough time, compound interest can theoretically turn even a relatively small amount of… …   Investment dictionary

• exponential growth phase — exponential growth phase. См. экспоненциальная фаза роста. (Источник: «Англо русский толковый словарь генетических терминов». Арефьев В.А., Лисовенко Л.А., Москва: Изд во ВНИРО, 1995 г.) …   Молекулярная биология и генетика. Толковый словарь.

• exponential growth — The exponential family of curves (Y = x) describes growth at an increasing (geometrical) ratio (as in the example of compound interest rates). Thomas Malthus (Essay on the Principle of Population, 1789) pointed out that if food resources increase …   Dictionary of sociology

• exponential growth — noun a) The growth in the value of a quantity, in which the rate of growth is proportional to the instantaneous value of the quantity; for example, when the value has doubled, the rate of increase will also have doubled. The rate may be positive… …   Wiktionary

• exponential growth — rate of growth which occurs at a constant percentage rate (Economics) …   English contemporary 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

### Share the article and excerpts

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