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(a) consider the initial-value problem a=ka,a(0)=ao as t as the model for the decay of a radioactive substance. show that, in general, the half-life t of the substance is t = -(ln 2)/k. (b) if a radioactive substance has the half-life t given in part (a), how long will it take an initial amount aoof the substance to decay to 01/6ad?

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