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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25-12-2017
Mathematics

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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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mathstudent55 mathstudent55 · Answer 1 · 2017-12-25T06:04:24+01:00

mathstudent55 mathstudent55

25-12-2017

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

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