Answer:
9155 years old
Explanation:
We use the following expression for the decay of a substance:
[tex]N = N_0\,\,e^{-k*t}[/tex]
So we first estimate the value of k knowing that the half-life of the C14 is 5730 years:
[tex]N = N_0\,\,e^{-k*t}\\N_0/2=N_0\,\,e^{-k*5730}\\1/2 = e^{-k*5730}\\ln(1/2)=-k*5730\\k= 0.00012[/tex]
so, now we can estimate the age of the artifact by solving for"t" in the equation:
[tex]1/3=e^{-0.00012*t}\\ln(1/3)= -0.00012*t\\t=9155. 102[/tex]
which we can round to 9155 years old.
