I have this data set: $x=[0.001,0.501,1.001,1.501,2.001,2.501,3.001,3.501,4.001,4.501,5.00]';\\y=[0.00007356,0.00000935493,0.00000356332,0.000001962,0.0000012741,0.000000903298,0.00000067154,0.000000511808,0.000000395035,0.000000306847,0.000000239228]';$
which gives the following plot
Using 'cftool' in Matlab,the above did not fit well as a single exponential but fits well as the sum of two exponentials (sorry I could not attach the plot) and the details are as follows: General model Exp2: $ f(x) = a*exp(b*x) + c*exp(d*x)$
Coefficients (with 95% confidence bounds): $ a = 7.178e-005 (6.002e-005, 8.354e-005)$, $ b = -3.831 (-5.012, -2.65)$, $ c = 1.72e-006 (-9.799e-006, 1.324e-005)$, $d = -0.594 (-3.79, 2.602)$.
Goodness of fit: $SSE: 9.431e-012$, $ R-square: 0.998$, $Adjusted\: R-square: 0.9972$, $RMSE: 1.161e-006$.
The problem is that I need to find the rate of decay. I have tried transforming the y-axis but it did not work maybe because it is the sum of two exponentials. Any assistance will be deeply appreciated.
The rate of decay is a function of x and would normal be defined as f'/f. Have you considered other models, say $a \exp(-b x^c)$ as this has one less parameter and may work OK. Try fitting log(y) to x, it should be clearer what is going on.