Solving Exponential equation with data

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Onkar Khadke
Onkar Khadke 2020-9-10
评论： Onkar Khadke 2020-9-11
Dear sir,
I want to find four unknowns(a,b,c,d) which would fit with the model as y = a*(1-exp(-b*x)) + c*(exp(d*x)-1).
I am attaching data herewith. Please help me in chosing initial guess for unknowns.
Please provide steps and code in case for me to get started and able to fit it with the model.
Thank you
  2 个评论
Alex Sha
Alex Sha 2020-9-11
1：
a -0.00353320943950358
b -0.00183821185934112
c -0.0092638389118119
d -0.00950908245890883
2：
a 0.00926383877006205
b 0.00950908267448672
c 0.00353320959565315
d 0.0018382118314121
Onkar Khadke
Onkar Khadke 2020-9-11
Can you tell me how did you got those a b c d values? If you have used any code then please share it, it will help me as I have to fit many other data points.

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Alan Stevens
Alan Stevens 2020-9-10
Try
a = 0.0093; b = 0.0095; c = 0.0035; d = 0.00185;
f = a*(1 - exp(-b*x)) + c*(exp(d*x) - 1);
plot(x,y,'o',x,f),grid
xlabel('x'),ylabel('y')
legend('data','function')
to get
However, the curve fitting toolbox shoud get an even better fit (I don't have the curve fitting toolbox, so did a rough fit outside of Matlab).
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Alan Stevens
Alan Stevens 2020-9-11
As I said, because I don't have MATLAB's curve fitting toolbox I used another piece of software (Mathcad) to do the fit. I then rounded the numbers to the values I listed in my earlier reply.

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