Answer:
The wood was cut approximately 8679 years ago.
Step-by-step explanation:
At first we assume that examination occured in 2020. The decay of radioactive isotopes are represented by the following ordinary differential equation:
(Eq. 1)
Where:
- First derivative of mass in time, measured in miligrams per year.
- Time constant, measured in years.
- Mass of the radioactive isotope, measured in miligrams.
Now we obtain the solution of this differential equation:


(Eq. 2)
Where:
- Initial mass of isotope, measured in miligrams.
- Time, measured in years.
And time is cleared within the equation:
![t = -\tau \cdot \ln \left[\frac{m(t)}{m_{o}} \right]](https://tex.z-dn.net/?f=t%20%3D%20-%5Ctau%20%5Ccdot%20%5Cln%20%5Cleft%5B%5Cfrac%7Bm%28t%29%7D%7Bm_%7Bo%7D%7D%20%5Cright%5D)
Then, time constant can be found as a function of half-life:
(Eq. 3)
If we know that
and
, then:




The wood was cut approximately 8679 years ago.