From: Xiaoguang Li (xli03@emory.edu)
Date: Fri Oct 15 1999 - 12:38:43 MDT
just a quickie regarding the apparent confusion about the terms
_polynomial_, _geometric_, and _exponential_. the following is my present
understanding of these words.
a _polynomial_ function looks something like f(x) = mx^n, where m
and n are constants.
an _exponential_ function takes the form f(x) = n^x, where n is
constant. thus, for every unit increase in x, one multiplies the "old" value
of f(x) by a constant -- namely n -- to obtain the "new" value of f(x);
ie. f(x) = f(x - 1) * n = [n^(x - 1)] * n = n^x.
finally, i first met the term _geometric_ in the context of
numerical series such as 1, 2, 4, 8, ... 2^x, in which one multiplies the
(n - 1)th term by a constant -- in this case 2 -- to derive the nth term.
therefore, the interchangeability of the terms _exponential_ and
_geometric_ seems well justified. the _polynomial_, on the other hand, is
a very different beast.
xgl
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