Textbook Problem

Carbon Dating In Exercises 79–82, you are given the ratio of carbon isotopes to carbon atoms in a fossil. Use the information to estimate the age of the fossil. In living organic material, the ratio of radioactive carbon isotopes to the total number of carbon atoms is about 1 to 10¹². (See Example 3 in Section 4.1.) When organic material dies, its radioactive carbon isotopes begin to decay, with a half-life of about 5715 years. So, the ratio R of carbon isotopes to carbon-14 atoms is modeled by $R={10}^{-12\left(\frac{1}{2}\right)t/5715}$, where t is the time (in years) and t = 0 represents the time when the organic material died.

$R=0.13\times {10}^{-12}$