## help creating a function that has an x-axis bound (goes to infinity at a certain value) [closed]

I'm an engineer and my math is pretty rusty so please bear with me.

We need a function that approaches infinity at a given bound (however the bound is an input to the function, so basic polynomial interpolation did not work for us). We think this would be a variant of a vertical asymptote function.

The purpose of the function will be to calculate a price which increases similar to a linear function at first, but then as supply reaches a bound, it goes to infinity.

We came up with something that is close:
$p = (d-L-3)/(d-L) -3/L -i -1$

where:
p : current price
d : demand (units in circulation)

L : supply limit threshold
i : initial price

For example, here is a graph with L=50 and i=10:
http://juzzam.org:9090/example/GraphFunction/

The problem is it is too "flat" or "steep" for different input values. We want the price to double midway to the bound and triple at about 75%.

We tried adjusting constants, even if we get it correct for a specific (i,L) input value pair, it is incorrect for other input values.

Help!

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You will find in the FAQ at mathoverflow.net/faq#whatnot a short list of other sites where you can get math help. This site has a rather different objective. – Mariano Suárez-Alvarez Feb 24 2010 at 20:35
Hmm. Please look up "Lagrange interpolation". Thus, with a few test values, you can approximate it to a rational function. – Regenbogen Feb 24 2010 at 20:46
We tried polynomial interpolation but the bound can move (as it is an input value). Perhaps, we missed something.. I'll look into it more. Thanks for your help, and sorry for posting here. – Juzzam Feb 24 2010 at 21:00
Closed, please follow the links in Mariano's comment for suggestions of websites that will be more helpful to you. – Scott Morrison Feb 24 2010 at 21:01