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];

$ 
\frac{-2.10241 x^2-1735.16 x-43612.1}{x^{2.25431}+116.08 x+1843.92}
$

     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