Exponential

4 definitions found

From The Collaborative International Dictionary of English v.0.48 [gcide]:

  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]

From WordNet (r) 2.0 [wn]:

  exponential
       adj : of or involving exponents; "exponential growth"
       n : a function in which an independent variable appears as an
           exponent [syn: {exponential function}]

From Moby Thesaurus II by Grady Ward, 1.0 [moby-thes]:

  39 Moby Thesaurus words for "exponential":
     algorismic, algorithmic, aliquot, cardinal, decimal, differential,
     digital, even, figural, figurate, figurative, finite, fractional,
     imaginary, impair, impossible, infinite, integral, irrational,
     logarithmic, logometric, negative, numeral, numerary, numerative,
     numeric, odd, ordinal, pair, positive, possible, prime, radical,
     rational, real, reciprocal, submultiple, surd, transcendental
  
  

From The Free On-line Dictionary of Computing (27 SEP 03) [foldoc]:

  exponential
       
          1.  A function which raises some given constant
          (the "base") to the power of its argument.  I.e.
       
          	f x = b^x
       
          If no base is specified, {e}, the base of {natural
          logarthim}s, is assumed.
       
          2.  {exponential-time algorithm}.
       
          (1995-04-27)