SOLUTION: 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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: 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       Log On


   

Question 471331: 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.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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)
Where
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%2F100
2^(-t/5730) = .81
find the nat log of both sides
ln(2^(-t/5730)) = ln(81)
log equiv of exponents
-t%2F5730ln(2) = ln(81)
-t%2F5730 = ln%2881%29%2Fln%282%29
-t%2F5730 = -.304
multiply both sides by -5730, results
t = 1,742 yrs