Answer:
The age of the earliest known human-like footprints is approximately 3000000 years.
Step-by-step explanation:
Decay of isotopes is represented by the following ordinary differential equation:
(Eq. 1)
Where:
- First derivative of mass with respect to time, measured in miligrams per year.
- Current mass of the isotope, measured in miligrams.
- Time constant, measured in years.
Now we proceed to obtain the solution of the differential equation:
(Eq. 2)
Where:
- Initial mass of the isotope, measured in miligrams.
- Time, measured in years.
- Time constant, measured in years.
We proceed to clear time within the formula presented above:
In addition, time constant can be found as a function of half-life:
(Eq. 3)
If we know that
,
and
, the age of the earliest known human-like footprints is:
The age of the earliest known human-like footprints is approximately 3000000 years.