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Half-lives are the result of (mathematical) exponential decay of the form Ae^-kt, where A is the amount you start with, t time and k is some value specific to the isotope in question (and e is Euler's number, of course). The linear term is in the exponent. None of the derivatives are constant - I don't think I said that. But the amount of time it takes for half of any given amount to decay is constant, which is what I intended to convey. If we assume that (continuing your marbles metaphor) everybody starts out with 1024 marbles, we can determine how long they've been losing their marbles by how many they have left. That is the gist of carbon dating (or any of the other similar radio-dating methods). Of course, with 14C they have discovered a few anomalous years where 14C seems to have been produced in substantially larger quantities than typically, perhaps due to solar activity or some star going nova somewhere, making 14C dating less accurate than it is portrayed, but that is a side note.