In the absence of additional information about the form, and just eyeballing the shape makes it look like a rational polynomial-ish thing, I vote for...

    nlf = NonlinearModelFit[data, (c0 + c1 x + c2 x^2)/(c3 + c4 x + x^c5), {c0, c1, c2, c3, c4, c5}, x];

>(-43612.1 - 1735.16 x - 2.10241 x^2)/(1843.92 + 116.08 x + x^2.25431)

     nlf["AdjustedRSquared"]
     nlf["FitResiduals"] // MinMax

> 0.999999

> {-0.0134303, 0.014954}

     Plot[nlf[x], {x, 1, 300}, Epilog -> Point[data]]
[![enter image description here][1]][1]


  [1]: https://i.stack.imgur.com/sIvJY.jpg