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:
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.