Name: Dave E.
Where is the value e, the base of the natural
logarithms, found in nature?
The number 'e' appears in many applications and circumstances in nature.
It is so ubiquitous that listing all these in not practical. For some
examples do an internet search on: "number e". I prefer the search engine
www.google.com but you can use any one.
As a generality ANY PROCESS in which the rate of change of a variable Y(x),
delta Y(x)/delta x, is proportional to the value of Y(x) results in Y(x)
being an exponential function of (x). That is: Y(x) = A*e^(k*x) where 'A'
and 'k' can be either positive or negative depending upon the process.
Some specific examples are the compounding of interest, and radioactive
The number 'e' occurs in many places in nature.
Any process, of which there are many, where the rate of change is
proportional to the amount of whatever is changing in the process will
involve e^(some power or function. The rate of many chemical reactions is an
example, as is the decay of radioactive nucleii. The temperature dependence
of the vapor pressure of liquids is obeys an exponential law [Clausius
Clapyeron equation]. The absorption of many substances by the body often
obeys this dependence.
The list is long.
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Update: June 2012