decay rate of data in matlab - matlab

Question

I want to know how quickly some data returns to baseline after an initial peak (here at ca x=5);
The quadratic fit looks about right (from the figures option of matlab, shown below) - but I'm looking for a concise quantification of this curve, therefore I presume the 'decay rate' of the exponential function would be one very straightforward.
Is this assumption correct?
If yes, I looked at the formula on wiki for this, and attempted shamelessly to find a solve for the time constant (but unsuccessfully so). Can someone help me out, or is this actually a not so trivial problem?
edit: I was planning to find the peak using MathWorks' findpeaks() function, and the lowest point of the curve using the 'inverse' findpeaks() (as in: -y)
%approx data values of the curves below
y= [0 0.07 0.08 0.08 0.08 0.06 0.06 0.05 0.04 0.05 0.04 0.02 0.01 0.02 0.01 0.01 0.03 0.02 0.02 0.02 0.03 0.01 0.02 0.01 0.01 0.03 0.02 0.01 0.02 0.01];
x=1:numel(y);
plot(x,y);

Answer 1

These are the two options I was looking for, maybe someone can elaborate / improve this answer about the differences for these approaches - for me this is good enough, thanks for the comments. Before this step, using the data provided in the example of the question, the local maximum and minimum has to be extracted, this can be done easily using findpeaks()
approach 1) requires the curve toolbox from Matlab [Source]
%Fit a Single-Term Exponential Model, copy from Mathworks documentation, all credits go there
x = (0:0.2:5)';
y = 2*exp(-0.2*x) + 0.1*randn(size(x));
f = fit(x,y,'exp1')
f =
General model Exp1:
f(x) = a*exp(b*x)
Coefficients (with 95% confidence bounds):
a = 2.021 (1.89, 2.151)
b = -0.1812 (-0.2104, -0.152)
plot(f,x,y)
or approach 2) requires the optimizaion toolbox from Matlab [Source]
%copy from Mathworks documentation, all credits go there
rng default % for reproducibility
d = linspace(0,3);
y = exp(-1.3*d) + 0.05*randn(size(d));
fun = #(r)exp(-d*r)-y;
x0 = 4;
x = lsqnonlin(fun,x0)
plot(d,y,'ko',d,exp(-x*d),'b-')
legend('Data','Best fit')
xlabel('t')
ylabel('exp(-tx)')