SOLUTION: Suppose a radioactive substance is decaying at a rate of 34% per year. Initially you have 500 grams of the substance. Explain why the amount of the radioactive substance is an e

Question 134649: Suppose a radioactive substance is decaying at a rate of 34% per year. Initially you have 500 grams of the substance.
Explain why the amount of the radioactive substance is an exponential function
Explain why the yearly decay factor is a =0.66.
Write a formula for the amount of the radioactive substance.
How many grams will be left after two years?
After how many years will there be only 11 grams left?
What is the monthly decay factor (to three decimal places)?
What is the monthly percentage decay rate?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Suppose a radioactive substance is decaying at a rate of 34% per year. Initially you have 500 grams of the substance.
A(t) = A(0)*0.66^t
Explain why the amount of the radioactive substance is an exponential function
Because each year there is 66% of what there was last year.
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Explain why the yearly decay factor is a =0.66.
66% of last years amount is how much of the material remains after one year.
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Write a formula for the amount of the radioactive substance.
A(t)= 500*0.66^t
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How many grams will be left after two years?
A(2) = 500*0.66^2 = 217.80 grams
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After how many years will there be only 11 grams left?
11 = 500*0.66^t
tlog(.66) = log(11/500)
t = [log(11/500)]/[log0.66]
t = 9.1855 years
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What is the monthly decay factor (to three decimal places)?
The yearly decay rate is 34%; The monthly decay rate is 0.34^(1/12) = 0.914
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What is the monthly percentage decay rate?
A(0) = 500
A(1/12) = 500*0.66^(1/12)= 482.9832
A(1/12)/A(0) = 482.9832/500 = 0.9660 (amount left after one month)
Monthly percentage decay rate = 1-0.9660 = 0.034 = 3.4%
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Cheers,
Stan H.
Qua

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