I regularly encounter a type of curve which cannot be easily expressed using a simple curve equation (e.g. trendlines available in Excel). See attached the example curve data. In the spreadsheet I had begun to try fitting an exponential approach-type curve, though to little avail.

Curves.xls

I was wondering whether the great minds of this forum knew of a better curve type that could characterise this data? I'm trying to avoid using high-order polynomials as they seem to be unreliable and the shape of the curves are, in reality, controlled by just a handful of parameters (4 to 6 inputs at most). The example data in the spreadsheet provides a range of different shapes to try fitting an equation to; if one type of equation works for all four examples, then I imagine it will work on all my other examples.

Thanks in advance for any help with this curve fitting!