I'm looking for the equation that fits the data listed below.  What is
the equation that best fits this data?  y=f(x)??  On log log paper,
the curve appears like the equation 1-e^(-ax) appears on linear linear
paper.

x	y
0.0012	0.002
0.0014	0.022
0.0016	0.044
0.002	0.089
0.003	0.2
0.004	0.31
0.006	0.44
0.008	0.54
0.01	0.61
0.02	0.84
0.04	0.93
0.1	1
1	1

The equation must converge to 1 for large x values.

Hello Tmall

I have used the excellent Curve Expert to compile this list of
possible solutions to your data points listed above.  This software
can be downloaded from http://www.ebicom.net/~dhyams/cvxpt.htm and
will draw graphs of each of the possible solutions for you.  I would
highly recommend at least taking a look at this piece of software (if
not purchasing it).

An alternative way to look at the data would be to use the zunzun.com
website although this is considerably more complicated to use.

According to the Curve Expert software the best fit lines for your
data are (further statistics are available by using the software):

1) Weibull Model: y=a-b*exp(-c*x^d)
a = 0.99494109
b = 1.304623
c = 36.304995
d = 0.73432375
Standard Error: 0.0122013
Correlation Coefficient: 0.9996236
Comments: The fit converged to a tolerance of 1e-006 in 8 iterations.
No weighting used.

2) MMF Model: y=(a*b+c*x^d)/(b+x^d)
a = -0.10882534
b = 0.0010501178
c = 1.0145978
d = 1.3492462
Standard Error: 0.0123243
Correlation Coefficient: 0.9996159
Comments: The iteration count of 100 was exceeded.  The fit failed to
converge to tolerance of 0.000001 (CHI2 at 0.001367). No weighting
used.

3) Vapor Pressure Model: y=exp(a+b/x+cln(x))
a = 0.011797156
b = -0.0053048177
c = -0.014056123
Standard Error: 0.0154654
Correlation Coefficient: 0.9993279
Comments: The fit converged to a tolerance of 1e-006 in 3 iterations.
No weighting used.

4) Modified Hoerl Model: y=a*b^(1/x)*x^c
a = 1.0118677
b = 0.99470924
c = -0.014055661
Standard Error: 0.0154654
Correlation Coefficient: 0.9993279
Comments: The fit converged to a tolerance of 1e-006 in 3 iterations.
No weighting used.

5) Rational Function: y=(a+bx)/(1+cx+dx^2)
a = -0.25241261
b = 194.96896
c = 176.8517
d = 17.203241
Standard Error: 0.0171513
Correlation Coefficient: 0.9992561
Comments: The fit converged to a tolerance of 1e-006 in 8 iterations.
No weighting used.

6) Modified Exponential: y=a*e^(b/x)
a = 1.0375904
b = -0.005013615
Standard Error: 0.0181261
Correlation Coefficient: 0.9989843
Comments: The fit converged to a tolerance of 1e-006 in 3 iterations.
No weighting used.

7) Root Fit: y=a*b^(1/x)
a = 1.0375904
b = 0.99499893
Standard Error: 0.0181261
Correlation Coefficient: 0.9989843
Comments: The fit converged to a tolerance of 1e-006 in 3 iterations.
No weighting used.

8) Exponential Association (3): y=a(b-exp(-cx))
a = 1.1097553
b = 0.87861712
c = 116.13166
Standard Error: 0.0227064
Correlation Coefficient: 0.9985507
Comments: The fit converged to a tolerance of 1e-006 in 6 iterations.
No weighting used.

All of these models give excellent correlation coefficients and small
standard errors.  Perhaps the 'simplest' of these possible solutions
is the root fit (#7).

If you require any further information please ask for clarification
and I will do my best to help.

Exactly what I was looking for and in a very timely manner.  Thanks