Question 179440: Hello dear tutor,
I need help with a certain math problem today that we just learned in class, but I can only get how to do really with like an actual example from my homework, which is why I am here, trying to learn! So here is the question! Thanks so much for helping out! it means ALOT!
Radon-222 is a gas that escapes from rocks and soil. It can accumulate in buildings and can be dangerous for people who breathe it. Radon-222 decays to polonium and eventually to lead.
a. Find the percent decrease in the amount of radon-222 each day.
b. Write an exponential decay function for th amount of a 500 mg sample of radon-222 remaining after t days.
c. How much of the radon-222 sample would remain after 14 days?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! You left this out of your post but it is essential information for your problem: "The most stable isotope, 222Rn, has a half-life of 3.8 days"
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Radon-222 is a gas that escapes from rocks and soil. It can accumulate in buildings and can be dangerous for people who breathe it. Radon-222 decays to polonium and eventually to lead.
a. Find the percent decrease in the amount of radon-222 each day.
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Percent means per hundred
So set up a proportion and solve for "x":
x/100 = (1/2)/3.8
Cross-multiply to get:
3.8x = 50
x = 12.88
Ans: 12.88%
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b. Write an exponential decay function for the amount of a 500 mg sample of radon-222 remaining after t days.
General Formula: A(t) = A(0)*(1/2)^(t/3.8)
Your problem:
A(t) = 500(1/2)^(t/3.8)
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c. How much of the radon-222 sample would remain after 14 days?
A(14) = 500(1/2)^(14/3.8)
A(14) = 500(1/2)^3.6842..
A(14) = 500*0.0777933...
A(14) = 38.8967.. mg
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Cheers,
Stan H.
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