SOLUTION: A wooden artifact from an archaeological dig contains 80 percent of the Carbon-14 that is present in living trees. To the nearest year, about how many years old is the artifact? (T

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: A wooden artifact from an archaeological dig contains 80 percent of the Carbon-14 that is present in living trees. To the nearest year, about how many years old is the artifact? (T      Log On


   

Question 1152999: A wooden artifact from an archaeological dig contains 80 percent of the Carbon-14 that is present in living trees. To the nearest year, about how many years old is the artifact? (The half-life of Carbon-14 is 5730 years.)
yr
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A wooden artifact from an archaeological dig contains 80 percent of the Carbon-14 that is present in living trees.
To the nearest year, about how many years old is the artifact?
(The half-life of Carbon-14 is 5730 years.)
:
The radiation decay formula
A+=+Ao%2A2%5E%28-t%2Fh%29, where
A = resulting amt after t time
Ao = initial amt of the substance
t = time of decay
h = half-life of substance
:
let Ao = 10 and A = 8
:
10%2A2%5E%28-t%2F5730%29+=+8; (t is the numerator)
2%5E%28-t%2F5730%29+=+8%2F10
2%5E%28-t%2F5730%29+=+.8
using natural logs
-t%2F5730ln(2) = ln(.8)
%28-t%2F5730%29+=+ln%28.8%29%2Fln%282%29
using your calc
%28-t%2F5730%29+=+-.3219
t = -5730 * -3219
t = 1845 yrs