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Question 1048802: Please help me with this question.
2. The rate of decay of a radioactive substance is 0.1% per year.
(a) Find the half-life of the substance.
(b) How long would it take until only 1/2 of the amount remains?
(c) How long would it take until 2/3 of the original amount decays?
(d) How much of the 10 mg sample of the substance will remain after
5,000 years?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The rate of decay of a radioactive substance is 0.1% per year.
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(a) Find the half-life of the substance.
A(t) = Ao(0.999)^t
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(b) How long would it take until only 1/2 of the amount remains?
(1/2)Ao = Ao(0.999)^t
0.999^t = (1/2)
t = log(0.5)/log(0.999) = 692.8 years
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(c) How long would it take until 2/3 of the original amount decays?
t = log(2/3)/log(0.999) = 405.26 years
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(d) How much of the 10 mg sample of the substance will remain after
5,000 years?
A(5000) = 10*0.999^5000
A(5000) = 0.0672 mg
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Cheers,
Stan H.
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