LETTERS TO THE EDITORS

# Your Number's Up

To the Editors:

In discussion of the Lambert *W* function (*Computing
Science,* March–April), Brian Hayes offers as description
of the Euler number *e*, the limiting value of a compound
interest expression.

As a physical chemist, I would observe that there are a number of
natural decay processes that *e* well describes, including
first order chemical rate processes, radioactive decay, and
electrical RC circuit behavior.

All of these result from integration over time of the differential
equation, *–dX/dt = kX*, where *X* is some
physical quantity (concentration, charge) and *k* is a rate
constant. The result is *X = e ^{(–kt)}*,
leaving out the constant of integration.

Thus, I suggest that *e* is not merely some useful
mathematical construct, but a description of some widespread natural phenomena.

David M. Wetstone

Hartford, Connecticut

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