SOLUTION: to the nearest full day determine how long it will take for 400 millicuries of I-131, which has a half life of 8 days, to decay to 3.125 millicuries?

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Question 275217: to the nearest full day determine how long it will take for 400 millicuries of I-131, which has a half life of 8 days, to decay to 3.125 millicuries?
Answer by ankor@dixie-net.com(22740) (Show Source):
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to the nearest full day determine how long it will take for 400 millicuries of I-131, which has a half life of 8 days, to decay to 3.125 millicuries?
:
The half-life equation Ao*2^(-t/h) = A
Where
A = resulting amt
Ao = initial amt
t = time (in days in this application)
h = half-life of the substance
:
400 * 2^(-t/8) = 3.125
Divide both sides by 400
2^(-t/8) =
2^(-t/8) = .0078125
:
ln(2^(-t/8)) = ln(.0078125)
:
*ln(2) = ln(.0078125)
= ; enter in your calc
= -7
t = -7 * -8
t = 56 days
;
:
Check this on a calc: enter 400 * 2^(-56/7) results: 3.125