SOLUTION: I'm having trouble figuring out the percentage of carbon-14. If soil was found to have lost 12% of it's carbon-14, then how old was the soil?

Question 303897: I'm having trouble figuring out the percentage of carbon-14. If soil was found to have lost 12% of it's carbon-14, then how old was the soil?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
percentage of carbon-14.
If soil was found to have lost 12% of it's carbon-14, then how old was the soil?
:
They should give you the half-life of Carbon 14. Most sources say it's 5730 yrs
:
The decay formula: A = Ao*2^(-t/h)
where
A = resulting amt after t yrs
Ao = initial amt (t=0)
t = time in yrs
h = half-life of substance (5730 yrs in this case)
:
Let Ao = 1, then remaining amt (A) after t yrs: 1 -.12 = .88 (lost 12%)
:
1*2^(-t/5730) = .88
using nat logs
ln[2^(-t/5730)] = ln(.88)
log equiv of exponents
*ln(2) = ln(.88)
*.693 = -.128
=
= -.1844
t = -5730 * -.1844
t = 1057 yrs old
;
:
Check solution on a calc: enter 2^(-1057/5730) = .8799 ~.88 or 88% remaining

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