SOLUTION: an artifact was found and tested for its carbon-14 content. if 77% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? use that carbon

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Question 473415: an artifact was found and tested for its carbon-14 content. if 77% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? use that carbon-14 has a half-life of 5,730 years.
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
The general exponential decay function is: Pt+=+Po%2Ae%5E%28kt%29
Given is that the half-life is 5730. This means that t=5730 when Pt%2FPo+=+1%2F2
We can solve for k:
e%5E%285730k%29+=+1%2F2
Take natural log of both sides
5730k+=+ln+%281%2F2%29
Divide by 5730 on both sides
k+=+ln%281%2F2%29%2F5730
Now substitute this value in for k into general equation, along with fact that Pt%2FPo+=+0.77
Solve for t:
e%5E%28ln%281%2F2%29%2F5730%2At%29+=+0.77
Take natural log of both sides
ln%281%2F2%29%2F5730%2At+=+ln+0.77
Multiply by reciprocal -> 5730/ln(1/2)
t+=+%285730%2Aln+0.77%29%2Fln%281%2F2%29
Use scientific calculator to estimate answer, round to nearest hundred
t = 2,200 years