Exponential
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 — may refer to any of several mathematical topics related to exponentiation, including: *Exponential function, also: **Matrix exponential, the matrix analogue to the above *Exponential decay *Exponential growth *Exponential map, in differential… …   Wikipedia

  • exponenţial — EXPONENŢIÁL, Ă, exponenţiali, e, adj. (mat.) Care are un exponent (2) variabil, nedeterminat sau necunoscut. ♦ (Despre funcţii) A cărei variabilă independentă apare într un exponent. [pr.: ţi al] – Din fr. exponentiel. Trimis de ana zecheru,… …   Dicționar Român

  • exponential — ex‧po‧nen‧tial [ˌekspəˈnenʆl◂] adjective ECONOMICS exponential growth/​increase/​rise etc a rate of growth that becomes faster and faster over time: • Tropical diseases are becoming more common in affluent parts of the world due to an… …   Financial and business terms

  • exponential — 1704, from EXPONENT (Cf. exponent) + AL (Cf. al) (1). As a noun, from 1784. Related: Exponentially …   Etymology dictionary

  • exponential — ► ADJECTIVE 1) (of an increase) becoming more and more rapid. 2) Mathematics of or expressed by a mathematical exponent. DERIVATIVES exponentially adverb …   English terms dictionary

  • exponential — [eks΄pō nen′shəl, eks΄pō nen′chəl] adj. 1. Math. a) of or relating to an exponent b) involving a variable or unknown quantity as an exponent 2. of or increasing by extraordinary proportions exponentially adv …   English World dictionary

  • exponential — adjective Date: 1704 1. of or relating to an exponent 2. involving a variable in an exponent < 10x is an exponential expression > 3. expressible or approximately expressible by an exponential function; especially characterized by or being an… …   New Collegiate Dictionary

  • Exponential — Die Mathematik bezeichnet als Exponentialfunktion eine Funktion der Form mit der Basis . In der gebräuchlichsten Form sind dabei für den Exponenten x die reellen Zahlen zugelassen. Im Gegensatz zu den Potenzfunktionen, bei denen die Basis die… …   Deutsch Wikipedia

  • exponential — ex|po|nen|tial [ˌekspəˈnenʃəl] adj technical 1.) exponential growth/increase etc exponential growth, increase etc becomes faster as the amount of the thing that is growing increases ▪ an exponential increase in travel 2.) using a small number or… …   Dictionary of contemporary English

  • exponential — ex·po·nen·tial .ek spə nen chəl adj expressible or approximately expressible by an exponential function <an exponential growth rate> ex·po·nen·tial·ly nench (ə )lē adv * * * ex·po·nen·tial (ek″spə nenґshəl) denoting a… …   Medical dictionary

Share the article and excerpts

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