from
The Collaborative International Dictionary of English v.0.48
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]