The amount of a sample remaining after t days is given by the equation cap p times t is equal to cap A times 1 half raised to the t over h power , where cap A is the initial amount of the sample and h is the half-life, in days, of the substance. A scientist has a 10 -mg sample of a radioactive isotope. The isotope has a half-life of 8 days. After 16 days, how much of the radioactive isotope remains?
Use the decay formula with an initial amount of 10 mg, a half-life of 8 days, and 16 days elapsed: 10 × (1/2)^(16/8) = 10 × (1/2)^2 = 2.5 mg. Two half-lives have passed, so the sample is reduced to one-quarter of its initial amount. The correct choice is A, 2.5 mg.
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