What should the ^14_6C content (in percent of y0) of a fossilized tree that is claimed to be 3000 years old?

The current mass fraction of should be approximately 68.8 percent.

Explanation:

is a radioactive isotope with a halflife of 5568 years. The decay of any radioisotope is modelled after the following ordinary differential equation:

Where:

- Current mass of the isotope, measured in grams.

- Time constant, measured in years.

The solution of this equation is of the form:

Where:

- Time, measured in years.

- Initial mass of the isotope, measured in grams.

The time constant can be found as a function of halflife ():

If and , the mass fraction of is:

The current mass fraction of should be approximately 68.8 percent.