Question 1065660: One of the main contaminants of a nuclear accident, such as that at Chernobyl, is strontium-90, which decays exponentially at an annual rate of approximately 2.8% per year.
a. Write the percent of strontium-90 remaining, P, as a function of years, t, since the nuclear accident.
b.Estimate the half-life of strontium-90.
c.After the Chernobyl disaster, it was predicted that the region would not be safe for human habitation for 105 years. Estimate the percent of original strontium-90 remaining at this time.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! The general form of the exponential decay formula is
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y = a(1-b)^x where y is final amount remaining after x time, a is the original amount and b is the rate of decay
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for our problem we have
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P = a * (1 - 0.028)^t / a
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a) P = (1 - 0.028)^t
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b) 0.50 = 0.972^t
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use definition of logarithm
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t = log(0.972) (0.50)
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t = 24.401 approx 24.4 years
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c) P = 0.972^105
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P = 0.05069 approx 0.05 or 5%
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