t(s) = 1 15 30 45 60 75 90 105 120 135
N(counts) = 106 80 98 75 74 73 49 38 37 22
Consider a decaying radioactive source whose activity is measured at intervals of 15 seconds. the total counts during each period are given. What is the lifetime τ of the source? What are the uncertainties on N_0 and τ?
N(t) = N_0*exp(-t/τ)
The Attempt at a Solution
ln[N(t)]=ln[N_0]+(-t/τ) gives an affine function, so if I plot it I can get N_0 and τ from the graph. However this doesn't feel satisfactory to me, I'd prefer to do it mathematically, but I can't figure it out. I don't know how to do a linear fit for a Poisson distributed set of data. I think the error on the N(t) is given by (σ/√n) where n is the number of data points and σ=√avg[N(t)]. Any help?