Fitting exponential curve in data

I have a txt file with data corresponding to the number of atoms trapped as a function of time. How can I create a function (in a separate file) with

EDecay(t,τ,A,B) = A*exp(-t/τ)+B and then use the function fit to fit the data, using certain starting points? And then how can I deduce the lifetime τ?

Answer 1

[Matt J]

A more efficient and direct way would be to use fminspleas (Download)

load data

funlist={@(tau,t)exp(-t/tau),1};

idx=tdata>0;

[tau,AB]=fminspleas(funlist,1,tdata(idx),ydata(idx));

tau,

tau = 3.0246

A=AB(1),

A = 9.8728e+05

B=AB(2)

B = 2.5888e+04

fn=@(t) A*funlist{1}(tau,t)+B;

plot(tdata,ydata,'o', tdata, fn(tdata));
xlabel 't';
ylabel 'EDecay';
ylim([0,2*max(ydata)])

[gps]

@Matt J thank you very much, this method does work, but would it also be possible to see how this can be achieved by creating a separate file with the function EDecay and using the fit function?

[Matt J]

Why? If it works, why do more work than is necessary?