This seems less like a matlab question than a generic math/data analysis question. What produced these data? Generally I would think you would have some prior expectation of what functional form to expect.
If you simply need a function which follows the data in this domain, then just use interp, but if you need to use the parameters, then your functional form is fix by those requirements, and deviation from it indicates a mismatch between the data and the expectation.
It sounds more like you just need a good interpolation though
