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Topic: Unusual behavior in "real world" functions
Replies: 3   Last Post: Feb 25, 1998 12:05 PM

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Elisse Ghitelman

Posts: 34
Registered: 12/6/04
Unusual behavior in "real world" functions
Posted: Feb 18, 1998 7:46 PM
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This is in response to a post of Sheila King's a few(?) days ago.

She pointed out that her husband often deals with "real world" phenomena
that have unusual behaviors as certain of the parameters become very large
or very small. What do the functions that describe these behaviors look like?

What I remember from my discussions with physics teachers and my own study
of science in college is that in fact, it is NOT that the functions behave
oddly at small (or large) values, but rather that assumptions are made
about the domains of the functions used to describe these phenomena. Often,
scientists will disregard some force because it is so much smaller than
another over the domain they're considering. However, if the domain were
expanded, the system would need to include other information which may be
relevant.

In fact, it may be that the behavior we're describing with a quadratic
function (and which fits pretty well with measurements) is really the
quotient of a fifth degree polynomial by a third degree polynomial but the
parameters are usually so "big" that we don't notice it.

An example like this is to look at logistic growth compared to exponential
growth when population is much below the limit. The two functions are not
very different, and the exponential growth curve fits the data reasonably
well.

I think it may be more important to help students understand the
assumptions we make when we model certain behaviors with mathematical
functions. They need to learn to evaluate how valid these models are when
we either interpolate or extrapolate from measured data.

Elisse Ghitelman
Newton North High School
Newton, MA, USA




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