exponential

exponent +‎ -ial

• (UK) enPR: ĕk-spō-nĕn'-chəl, IPA^(key): /ˌɛk.spəʊ.ˈnɛn.tʃəl/
• (US) enPR: ĕk-spō-nĕn'-chəl, IPA^(key): /ˌɛk.spoʊ.ˈnɛn.t͡ʃəl/

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exponential

1. (Can we verify⁽⁺⁾ this sense?) Relating to an exponent.
2. (mathematics) Expressed in terms of an exponent (power of a base), the base often being 10 or e.

   In base-10 exponential form, 1,000,000 is written as 10⁶.

   If not otherwise specified, "the" exponential function is normally understood to mean e^x.

3. (mathematics) Characterised by a rate of change that is proportional to the value of the varying quantity, or, equivalently, by a doubling or halving over successive fixed intervals of time or other parameter, described as exponential growth or exponential decay.

   There were two deaths on Monday, four on Tuesday, and eight on Wednesday. The rate of increase seems exponential.

   • 2013, Yvelyne Germain-McCarthy, Bringing the NCTM Standards to Life: Best Practices, High School, page 101:

     ... Students apply the definition of slope to various representations of growth functions to discover differences between exponential and constant rate of growth.

4. (Discuss⁽⁺⁾ this sense) (loosely) Characterised by a very rapid rate of change, especially increase, or merely a very large amount or degree.

   There's been an exponential rise in the number of crimes reported this year, compared to last year.

   • 2011, Michael Kiers, College Convo - Overview of College Admissions :

     If loans are not what you are looking for, then search for scholarships [...] I have been putting together scholarship letters for parents over the past decade, and there is an exponential amount of money to be had.

   • 2013, Daniel M. Gerstein, National Security and Arms Control in the Age of Biotechnology :

     It is also about an arms control forum that has been meeting just once every five years for decision making on topics that are moving with exponential velocity [...]

   • 2018 July 31, Alvin Carpio, “Is it time to automate politicians?”, in The Economist:

     Of course, one can creatively conjure up a host of things robot-politicians can do at exponential speed and scale, from shaking hands and kissing babies to handling the fundraising “robocalls” that frustrate American voters.

• In non-technical contexts, the term is sometimes used loosely to refer to any kind of very rapid change, especially increase. This usage is often discouraged unless the change in question is truly exponential; synonyms such as dramatic may be favored instead.

• nonexponential

exponential (plural exponentials)

1. (mathematics) Any function that has an exponent as an independent variable.

   Synonym: exponential function

• UCS - The World’s Population Hasn’t Grown Exponentially for at Least Half a Century
• “exponential”, in OneLook Dictionary Search.