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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.
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