SOLUTION: Sodium-24 is used for medical purposes. The half-life of sodium-24 is 14.9 h. A hospital buys 480 mg. After how long will 3.75mg remain?

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Question 933433: Sodium-24 is used for medical purposes. The half-life of sodium-24 is 14.9 h. A hospital buys 480 mg. After how long will 3.75mg remain?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The question description seems impractical. Is 14.9 hours too short a time to purchase the expected 480 miligrams?

A=Ie%5E%28-kt%29
%281%2F2%29=1%2Ae%5E%28-kt%29
ln%281%2F2%29=ln%281%29-kt%2Aln%28e%29
-kt=ln%281%2F2%29
k=-%281%2Ft%29ln%281%2F2%29
k=-%281%2Ft%29%28-ln%282%29%29
k=ln%282%29%2Ft
highlight_green%28k=ln%282%29%2F14.9%29.

The model becomes highlight%28A=480%2Ae%5E%28-0.4652t%29%29.

You need a solution for t.
ln%28A%29=ln%28480%29%2Bln%28e%5E%28-0.04652t%29%29
ln%28A%29-ln%28480%29=-0.04652t
ln%28480%29-ln%28A%29=0.04652t
highlight_green%28t=%281%2F0.04652%29ln%28480%2FA%29%29
Let A=3.75 and evaluate t.

t=104 hours.
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4 days 8 hours 30 minutes

CHECK: This should be 7 periods of halflife time.
14.9*7=104.3, checks.