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The starting point is Eq. (2) rewritten in its equivalent form (6). For the standard decay Eq. (6), when θ(t) is a constant θ 0 and the population corresponds to a discrete ensemble of members, as holds for microbial growth-decay, the characteristic time of the exponential decay 1/θ 0 corresponds algebraically to the "mean lifetime", ℓ 0, of the members in the ensemble.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com