SOLUTION: The half-life of carbon-14 is 5730 years. A bone is discovered which has 30 percent of the carbon-14 found in the bones of other living animals. How old is the bone? __________

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Question 273388: The half-life of carbon-14 is 5730 years. A bone is discovered which has 30 percent of the carbon-14 found in the bones of other living animals. How old is the bone?
____________ years
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
The half-life of carbon-14 is 5730 years.
A bone is discovered which has 30 percent of the carbon-14 found in the bones of other living animals.
How old is the bone?
:
The half-life formula
A = Ao*2^(-t/h)
where
A = amt after t yrs
Ao = initial amt
t = time
h = half-life of substance
:
Set the initial amt at 1, then the resulting amt = .3
:
2^(-t/5730) = .3
using nat logs
ln(2^(-t/5730)) = ln(.3)
log equiv of exponents
ln(2)= ln(.3)
=
= -1.737
t = -1.737 * -5730
t = 9,953 yrs
:
:
Check solution on a calc: enter 2^(-9953/5730) results: .29999 ~ .3 (30%)

SOLUTION: The half-life of carbon-14 is 5730 years. A bone is discovered which has 30 percent of the carbon-14 found in the bones of other living animals. How old is the bone? ___________