SOLUTION: This is not from a book, but I desperately need it answered in the next couple hours. I've tried all evening and cannot get the correct answer! Help! A radioactive element sodi

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Question 111072: This is not from a book, but I desperately need it answered in the next couple hours. I've tried all evening and cannot get the correct answer! Help!
A radioactive element sodium-24 has a half-life of 14 hrs. and is used to help locate obstructions of blood flow. A procedure requires 0.9 grams and is scheduled to take place in 43 hours. The rate of decay of sodium-24 is 5%.
What is the minimum amount of sodium-24 that must be on hand now?
At least ____ years. (Answer should be accurate to two decimal places.)
Thanks!
Found 2 solutions by stanbon, scott8148:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A radioactive element sodium-24 has a half-life of 14 hrs. and is used to help locate obstructions of blood flow. A procedure requires 0.9 grams and is scheduled to take place in 43 hours. The rate of decay of sodium-24 is 5%.
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A(t) = Ao(1/2)^(t/14)
0.9 = Ao(1/2)^(43/14)
0.9 = Ao[11.896189...]
Ao = 7.5654... grams (the amount you need now to have 0.9 grams in 43 hours)
What is the minimum amount of sodium-24 that must be on hand now?
7.5654...grams
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At least ____ years. (Answer should be accurate to two decimal places.)
Question: Years to do what?
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Cheers,
Stan H.

Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
43 hrs is slightly more than 3 half-lives, so you will need slightly more than .9*2^3 g

let x= amount needed ___ .9=x(.5^(43/14)) ___ .9(2^(43/14))=x