Question 83285: Question-2: A 100 grams of a radioactive substance is expected to decay exponentially to 50 grams in the course of 7 years.
(a) Write down the half-life, and the rate of decay of the radioactive substance.
(b) Write down the function N(t) representing the mass of the decaying radioactive substance after t years,
(c) How much of the substance is expected to remain after 14, 21, and 28 years, respectively?. How long would it take for the radioactive substance to decay to under 1 gram?.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A 100 grams of a radioactive substance is expected to decay exponentially to 50 grams in the course of 7 years.
(a) Write down the half-life, and the rate of decay of the radioactive substance.
The half-life is obviously 7 years.
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(b) Write down the function N(t) representing the mass of the decaying radioactive substance after t years,
A(t) = A(0)(1/2)^(t/7)
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(c) How much of the substance is expected to remain after 14, 21, and 28 years, respectively?.
A(14) = 100(1/2)^(14/7) = 100(1/2)^2 = 100*1/4 = 25 grams
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A(21) = 100(1/2)^(21/7) = 100(1/2)^8 = 12.5 grams
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A(28) = 100(1/2)^4 = 6.25 grams
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How long would it take for the radioactive substance to decay to under 1 gram?.
1 = 100(1/2)^(t/7)
0.01 = (1/2)^(t/7)
Take the log of both sides to get:
(t/2)log(0.5) = log0.01
t/2 = -2/log(0.5)
t/2 = 6.64
t = 13.29 years
To decay to under 1 gram it will more that 13.29 years.
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Cheers,
Stan H.
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