Solving Exponential equation with data

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

[Alex Sha]

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]

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.

Answer 1

[Alan Stevens]

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).

[Onkar Khadke]

Thank you for your response. Can you tell me how did you calculated a, b, c, d values? Please help me with that.

[Alan Stevens]

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.

[Onkar Khadke]

Alright. I am Thankful for the help.