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an artifact was found and tested for its carbon-14 content.
If 81% of the original carbon-14 was still present, what is it probable age(to the nearest 100yrs)?
use that carbon-14 has a half-life of 5730 yrs.
The half life formula: A = Ao*2^(-t/h)
A = resulting amt after t yrs
Ao = initial amt
t = time in yrs
h = half-life of substance
When we are dealing with percent we can use the initial amt of 100
100*2^(-t/5730) = 81
2^(-t/5730) = .81
find the nat log of both sides
ln(2^(-t/5730)) = ln(81)
log equiv of exponents
ln(2) = ln(81)
multiply both sides by -5730, results
t = 1,742 yrs