Finding a function to fit a curve.

Question

I would like to fit an equation to the curve shown below. A selection of the data points (x,y) are given too.

I have tried to fit equations $y = a \, e^{(-b \, x)}$ and $y = a x^{-b}$ using software minitab 19 without getting a good fit.

So if an equation can be found or suggested, that would be good.

{{1., 3.97364}, {3., 2.65259}, {5., 2.12207}, {7., 1.81891}, {9., 1.61681}, {11., 1.46983}, {21., 1.07533}, {31., 0.888459}, {41., 0.77407}, {51., 0.694874}, {61., 0.63588}, {71., 0.589742}, {81., 0.552379}, {91., 0.521322}, {101., 0.494974}, {201., 0.349951}, {301., 0.278213}, {401., 0.226841}, {501., 0.18593}, {601., 0.152562}, {701., 0.12521}, {801., 0.102766}, {901., 0.0843466}, {1001., 0.0692285}, {2001., 0.00960411}, {3001., 0.00133238}, {4001., 0.000184842}, {5001., 0.0000256433}, {6001., 3.5575110^-6}, {7001., 4.9353610^-7}, {8001., 6.8468610^-8}, {9001., 9.4986910^-9}}

Answer 1

Using Matlab's curve fitting tool, I got the following fit:

with the parameters as below:

General model Exp2:
     f(x) = a*exp(b*x) + c*exp(d*x)
Coefficients (with 95% confidence bounds):
       a =       3.513  (3.237, 3.788)
       b =     -0.1935  (-0.2215, -0.1655)
       c =      0.9278  (0.7994, 1.056)
       d =   -0.004471  (-0.006014, -0.002928)

and the goodness of fit as below:

Goodness of fit:
  SSE: 0.2513
  R-square: 0.9903
  Adjusted R-square: 0.9893
  RMSE: 0.09473

which seems reasonable.