Finding charactersitic time in decaying dataset


I have a dataset of N points with the x-axis in a log scale, representing time and the y-axis a correlation. The correlation decays and I want to interpolate, somehow, and find the value of t for which C has decay to C/N (N being any number >1, normally is “e” Euler’s constant, as it is the usual definition of the characteristic time-scale) i.e. interpolate the data and find the pre-image (t_c) of a given value C(t_c) = C(0)/N.