Answer :
Answer
7665 years
Procedure
Let N₀ be the amount of carbon-14 present in a living organism. According to the radioactive decay law, the number of carbon-14 atoms, N, left in a dead tissue sample after a certain time, t, is given by the exponential equation:
N = N₀e^(-λt)
where λ is the decay constant which is related to half-life (T1/2) by the equation:
[tex]\lambda=\frac{ln(2)}{t_{\frac{1}{2}}}[/tex]Here, ln(2) is the natural logarithm of 2.
The percent of carbon-14 remaining after time t is given by N/N₀.
Using the first equation, we can determine λt.
The half-life of carbon-14 is 5,720 years, thus, we can calculate λ using the second equation, and then find t.
[tex]\lambda=\frac{ln(2)}{5720}=1.211\times10^{-4}[/tex]Solving the second equation for t, and using the λ we have just calculated we will have
t= 7665 years