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]