Curve fitting an asymptote

I'm trying to come up with an equation that represents some data points. The curve that they make looks like an asymptote. I've tried using the various trendline methods in excel and also the curve fitting methods on Wolfram Alpha but none of them are satisfactory, especially if I try and extrapolate.

Do you know of any good methods that you would recommend in this scenario?

These are the data points:


X Y
202 2
201 2
126 3
101 4
87 5
78 6
72 7
67 8
63.5 9
60.5 10
58 11
56 12
54.5 13
50.5 16
49.5 17
47.5 19
46 21
44 24
42 28
40 33
38 39
37 44
36 48
35 54
34 61
33 69
32 79
31 91
30 104.5
29 124
28 147
27 177
26 216
25 268
24 338
23 436
22 574
21 777