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 sample contains 60 percent of its original amount of Fermium- 257 The half-life of Fermium- 257 is about 100 days. About how old is the sample?
Set the remaining fraction equal to 0.60: 0.60 = (1/2)^(t/100). Taking logarithms gives t = 100 × ln(0.60) / ln(0.50) ≈ 73.7 days, which rounds to about 74 days (choice D).
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