SOLUTION: Only 15% of the carbon-14 in a wooden bowl remains. How old is the bowl? (Carbon-14 has a half-life of 5,700 years.

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Question 962216: Only 15% of the carbon-14 in a wooden bowl remains. How old is the bowl? (Carbon-14 has a half-life of 5,700 years.
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Growth Model, y=I%2Ae%5E%28-kt%29

ln%28y%29=ln%28I%29-kt
ln%28y%29-ln%28I%29=-kt
kt=ln%28I%29-ln%28y%29
k=ln%28I%2Fy%29%2Ft
k=ln%281%2F0.5%29%2F5700
k=ln%282%29%2F5700
k=0.0001216
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Specific Growth Model for Carbon-14, highlight_green%28y=Ie%5E%28-0.0001216t%29%29.

How old is the bowl?
kt=ln%28I%29-ln%28y%29
t=ln%28I%2Fy%29%2Fk
Now, I=1,y=0.15.
Evaluate t.
t=ln%281%2F0.15%29%2F0.0001216
highlight%28t=15600%29, years.