Answer:
The age of that rock is approximately 353.3 million years.
Step-by-step explanation:
According to the statement, 29.3 percent of the original mass of Uranium-235 became Lead-207. We know that decay of isotopes is represented by the following ordinary linear differential equation:
(Eq. 1)
Where:
- Rate of change of mass in time, measured in grams per year.
- Current mass of the isotope, measured in grams.
- Time constant, measured in years.
The solution of this differential equation is:
(Eq. 2)
Where:
- Initial mass of the isotope, measured in grams.
- Time, measured in years.
And we solve the expression for time herein:

Besides, time constant can be calculated as a function of half-life. Please notice that half-life of Uranium-235 is 704 million years. The equation is presented below:
(Eq. 3)
Where
is the half-life of the isotope, measured in years.
If we know that
and
, then:




The age of that rock is approximately 353.3 million years.