i dindn t know about this software before.............
have some rest :-) but i know that your brain will continue to think about this problem. I m a biologist it happen to me the same :-)
Hmm. Well, I got the Excel Solver routine to fit this curve to your data using a "manual" least-squares fit, and it's terrible. Moreover, the "hyperbola" doesn't even approach the alleged asymptote, nor does it approach the x-axis! The idea is sound, I think, but I have an error in its execution. I've spent too much time on it today already, so I'm afraid it'll have to wait.
Very fun problem, though! Thanks for posting it.
I haven't forgotten you. Alas, I have no real news. I haven't gotten my hyperbolas to fit correctly, despite having verified the formulas in Excel. For some reason, my ansatz appears to break down at the scale you have for your data. That is, the parameters Excel comes up with and plots is matched by what Mathematica plots when I put those parameters in there. Something is rotten in the state of Denmark!
I really want to get this, but I think I'm missing something basic. These hyperbolas are extraordinarily difficult to work with.
Hopefully, I can find something simple and fix it.
Let us know, if you do a least squares fit and if the fit is good.
As has been pointed out already, a high-degree polynomial fit won't work well for the purpose of extrapolation. The polynomial only fits the points you tell it to, but further out (in the domain of extrapolation), the graph of the polynomial will likely begin to fluctuate.
If Ackbeet's model doesn't fit your data well, have you considered using an appropriate polynomial in the interpolation phase, and then appending a straight line to the right end-point of the graph of the polynomial in the extrapolation phase? I don't know if this extrapolates your data well enough, but if you end up trying this after Ackbeet's model, let me know.
I mean that you can use any nice function to interpolate, such as your polynomial from before. However, use only this function in the interpolation area. For extrapolation, I was thinking of joining the graph of the chosen function with that of a straight line. The interpolating function is shown in blue, while the straight line is shown in red: ImageShack® - Online Photo and Video Hosting