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Suppose that U^238 has a half life of 4.5 billion years, decaying (through a series of relatively short lived intermediate atoms) to Pb^206. In a certain mineral sample there are .31 times as many Pb^206 atoms as there are of U^238. If one assumes that the mineral deposit contained no Pb^206 when it was formed and that no lead or uranium have been added to or escaped from the sample (except through the natural decay process) how old is the sample?

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