What equation/distribution fits this data set?

[fenixtx423]

This is a data set that I am trying to fit an equation to. The best I have come up with is two exponential curves added together or the Weibull distribution, but neither are a perfect fit. Any ideas?
x y

15	3.51
30	3.1135
42.4	2.8287
60	2.5502
84.8	2.1883
120	1.8273
169.8	1.4503
240	1.1108
339.4	0.79024
480	0.54226
678.8	0.37759
960	0.26832
1357.6	0.16609
1920	0.09051
2715.2	0.057455
3840	0.032173

 

[stapel]

On what basis are you concluding that any model must be an exact fit?

 

[fenixtx423]

I am studying a natural phenomenon and across multiple data sets I have obtained this exact shape of curve (but scaled differently for each data set). You are correct, at this point I am just hoping that there is an equation that models this curve.

 

[HallsofIvy]

In general, you can't expect any theoretical distribution to fit a given data set perfectly. The best you can do is decide which distribution fits your data best, under whatever criterion you wish.

 

[Ishuda]

This is a data set that I am trying to fit an equation to. The best I have come up with is two exponential curves added together or the Weibull distribution, but neither are a perfect fit. Any ideas?
x y

15	3.51
30	3.1135
42.4	2.8287
60	2.5502
84.8	2.1883
120	1.8273
169.8	1.4503
240	1.1108
339.4	0.79024
480	0.54226
678.8	0.37759
960	0.26832
1357.6	0.16609
1920	0.09051
2715.2	0.057455
3840	0.032173

Have you tried any regression like
u = ln(x)
v = ln(y)
v = a u² + b u + c

EDIT: But that is (close to?) a Weibull, isn't it?

 

[fenixtx423]

I have been able to obtain an almost perfect fit using the following function:

c₁ * ( c₂ / (c₂ + X) )^c₃

where:
c1 = 3.92
c2 = 180.1
c3 = 1.5