Re: Examples of exponential growth phenomena in nature

From: Stephen Montgomery-Smith (stephen_at_math.missouri.edu)
Date: 02/07/05 

Date: Mon, 07 Feb 2005 04:43:35 GMT

squash@peoriadesignweb.com wrote:
> The subject says it all. I am looking for example other than population
> growth.
>

A slightly weird example - if you go off in a rocket which accelerates
at a constant rate (relative to itself), then to an observer on the
ground, at first your velocity will increase at a constant rate, but
then this rate will decrease as the velocity gets close to the velocity
of light.

But if you meaure how far you have traveled using the time from the
point of view of someone on the rocket (and remembering the time and
space dilation effects), then the distance traveled (distance measured
with respect to the initial rest velocity) goes something like
         d = c^2/a (cosh(ta/c)-1).
For small t this gives the usual formula - at^2/2, but as t gets large
this grows exponentially.

Stephen

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