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There is no need to question it, because for present purposes
it's immaterial. If all you are interested in are the half-life
values, you could shift every time in the data set by some
arbitrary amount and the results would be the same.
The fit only cares about the number of events in a given
interval, and the length of the interval is invariant with
respect to a time shift. Both ends of the interval get shifted.
This is an example of gauge invariance.
In the exponentials, shifting the time changes the prefactor out
front, but doesn't affect the shape of the curve or the