SOLUTION: The half-life of carbon-14 is 5730 years. This means that every 5730 years the amount is reduced by 50 percent. Assume there are three milligrams of carbon in a piece of wood. How

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: The half-life of carbon-14 is 5730 years. This means that every 5730 years the amount is reduced by 50 percent. Assume there are three milligrams of carbon in a piece of wood. How       Log On


   

Question 842021: The half-life of carbon-14 is 5730 years. This means that every 5730 years the amount is reduced by 50 percent. Assume there are three milligrams of carbon in a piece of wood. How much carbon-14 will be in the piece of wood 1000 years from now?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
A diagram in a wikipedia article suggests that for dead wood, the portion of carbon as C-14 is 3.6%. Your piece of wood would have an estimated %280.036%29%283%29=0.108 milligrams of C-14 now.

DECAY EQUATION
A=Ie%5E%28-kt%29, I initial amount, t years, A amount at t years, k a constant, e Euler Number
Half-Life A=I/2, so equation becomes I%2F2=Ie%5E%28-kt%29
%281%2F2%29=e%5E%28-kt%29 and we also expect t=5730 for this half-life,
%281%2F2%29=e%5E%28-k%2A5730%29
ln%281%2F2%29=-k%2A5730%2Aln%28e%29
-k%2A5730%2A1=ln%281%2F2%29
k=%28-ln%281%2F2%29%29%2F5730
highlight_green%28k=0.000121%29
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The decay equation may be highlight%28A=Ie%5E%28-0.000121%2At%29%29

Your question specifies a calculable 0.108 milligrams of Carbon 14 at present now, and to find how much will be present for t=1000 years.
-
I=0.108 and t=1000;
Find A.
highlight%28A=%280.108%29e%5E%28-0.000121%2A1000%29%29