Original Message (ID '85425') By sk597653: 
In Response To 'Re: Re: Re: Re: Re: Re: Re: Plotting nonlinear...'

Yet another incarnation:
c= 1.32
b = 1 + k c + k x/(2 s)
y2 = (b  (Sqrt[b^2  2 k^2 c x/s]))/(2 k )
Therefore
1 + 1.32 k + (k x)/(2 s)  Sqrt[((2.64 k^2 x)/s) + (1 + 1.32 k + (k x)/(2 s))^2])/(2 k)
modified data to read
data = {{0.0, 0.0}, {0.79333, 0.4176}, {1.19, 0.5385}, {1.5867,
0.6374}, {1.9833, 0.7473}, {2.38, 0.8571}, {2.7767,
0.9231}, {3.1733, 0.9560}, {3.57, 0.9780}, {3.9667,
0.9780}, {4.3633, 0.9890}, {4.76, 1.0220}, {5.1567,
0.9890}, {5.5533, 1.0110}, {6.3467, 1.0000}, {7.5367,
1.0000}, {8.7267, 1.0110}, {10.313, 1.0000}}
Hopefully this modification will correct for the magnitude of error in our resutlt. Now for:
fit = FindFit[data, y2, {k, s}, x]
And I get error:
FindFit::nrlnum: The function value {0. +0. I,0.497189+0. I,0.661709+0. I,0.807129+0. I,0.966744+0. I,1.12983+0. I,1.2531+0. I,1.34771+0. I,1.43645+0. I,1.50889+0. I,1.5988+0. I,1.7182+0. I,1.78024+0. I,1.90736+0. I,2.14485+0. I,2.66116+0. I,3.53309+0. I,7.8039+2.08105 I}
is not a list of real numbers with dimensions {18} at {k,s} = {0.0187691,0.134454}. >>
{k > 0.0187691, s > 0.134454}
Now, again with this exact data set, the k and s should be 2900000 and 0.84 respectively, that is what Sigmaplot gave. I do not have any of the information other than this from sigmaplot as this student is no longer here.
Furthermore, I did calculate by hand with the equation and data given. When I used 0.79333 as x, and the k and s previously discussed, I calculated y to be 0.47222, not bad, right?! Again I tried with the last data point, x= 10.313 and got y to be 1.31999. What is going on?!
Can you please try calculation as I did by hand. I don't think I made gross errors with my math as I reproduced it a couple of times and with different datapoints. So, for this data, and the given equation, a result of k=2900000 and s =0.84 does not seem far fetched! What is going on Mathematica? I know this should work. Any ideas with the newly modified formatting of the xaxis data?
Samantha

