SOLUTION: An anthropologist finds there is so little remaining Carbon-14 in a prehistoric bone that instruments cannot measure it. This means that there is less than 0.5% of the amount of Ca

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: An anthropologist finds there is so little remaining Carbon-14 in a prehistoric bone that instruments cannot measure it. This means that there is less than 0.5% of the amount of Ca      Log On


   

Question 475305: An anthropologist finds there is so little remaining Carbon-14 in a prehistoric bone that instruments cannot measure it. This means that there is less than 0.5% of the amount of Carbon-14 the bones would have contained when the person was alive. How long ago did the person die? Round your answer to the nearest thousand. (22,000, etc)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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An anthropologist finds there is so little remaining Carbon-14 in a prehistoric bone that instruments cannot measure it.
This means that there is less than 0.5% of the amount of Carbon-14 the bones would have contained when the person was alive.
How long ago did the person die? Round your answer to the nearest thousand. (22,000, etc)
:
The half life formula
A = Ao*2^(-t/h)
Where
A = remaining amt after t yrs
Ao = initial amt
t = time in yrs
h = half-life of substance
:
The generally accepted half-life for Carbon 14 = 5730 yrs
We can assume the initial amt = 1, the resulting amt =.005
:
2^(-t/5730) = .005
using nat logs
-t%2F5730ln(2) = ln(.005)
-t%2F5730 = ln%28.005%29%2Fln%282%29
-t%2F5730 = -7.6438562
t = -5730 * -7.6438562
t = 43,800 yrs