SOLUTION: The radioactive element carbon-14 has a half-life of 5750 years. The percentage of carbon-14 present in the remains of plants and animals can be used to determine age. How old is a

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Question 363543: The radioactive element carbon-14 has a half-life of 5750 years. The percentage of carbon-14 present in the remains of plants and animals can be used to determine age. How old is a skeleton that has lost 40% of its carbon-14?
Note: Do not round any numbers during your calculation.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The radioactive element carbon-14 has a half-life of 5750 years.
The percentage of carbon-14 present in the remains of plants and
animals can be used to determine age.
How old is a skeleton that has lost 40% of its carbon-14?
Note: Do not round any numbers during your calculation.
:
Using the half-life formula: A = Ao*2^(-t/h)
Where
A = resulting amt after t yrs
Ao = initial amt
t = time
h = half-life of substance
:
Assume the initial amt = 1, remaining amt after t yrs = .6
:
1*2^(-t/5750) = .6
using nat logs
-t%2F5750ln(2) = ln(.6)
-t%2F5750 = ln%28.6%29%2Fln%282%29
-t%2F5750ln(2) = -.736955942
t = -5750 * -.736955942
t = 4,237.55 yrs