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February 23rd, 2013, 03:05 PM   #1
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Modelling real life data

http://www.livoniapublicschools.org/web ... 2-2013.pdf
(please scroll down to page 7, for the problem "GOLD MEDAL HEIGHTS")

In brief, I am asked to find a model function for the real life data.

I am currently experimenting with quintic functions (degree 5) as there are 4 local max/mins, but there's an obvious limitation as the y values reaches positive and negative infinity as x -> +infinity and x -> -infinity. This is impossible in real life as human jump heights will reach a biological maximum limit (and impossible to jump a negative height).

I was also thinking of a step wise function, where after a quintic function, I add onto a logarithm function as to introduce a horizontal asymptote.

As well, I was thinking of a sigmoid function, as this is a biological data.
Maybe even arc tan function... (but I have no idea what that is)

My teacher has been absent for the last couple of weeks due to health issues, and the substitute doesn't know any math. As such, I have been working on this by myself for a week now, and I am stuck.

Any help will be appreciated
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February 25th, 2013, 10:56 AM   #2
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For 1952 onwards, and just for fun, height = 250 - 928/(year - 1932).
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