The decay rate for a radioactive isotope is 9.29.2 percent per year. find the half-life of the isotope. round to the nearest tenth of a year.

Question

Mathematics

Adriel Jones

21 January, 10:23

The decay rate for a radioactive isotope is 9.29.2 percent per year. find the half-life of the isotope. round to the nearest tenth of a year.

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Answers (1)

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Abbie Stark · Answer 1

Exponential decay is given by the equation

F = P (1 - r) ^t

0.5 = 1 (1 - 0.092) ^t

0.5 = (0.908) ^t

log 0.5 = log (0.908) ^t

log 0.5 = t * log 0.908

t = (log 0.5) / (log 0.908)

t = 7.18

Answer: 7.2 years