A fossil has 25% of its original carbon-14 remaining. Using a carbon-14 half-life of 5730 years, estimate its age.

Solution & explanation

1. Given: Remaining fraction = 25%; T½ = 5730 years.

2. Convert percentage to a fraction.

   $$\frac{N}{N_0}=\frac{25}{100}=\frac{1}{4}$$

3. After one half-life, half remains; after two, a quarter remains.

   $$\frac{1}{4}={\left(\frac{1}{2}\right)}^2$$

4. Thus two half-lives have elapsed.

   $$n=2$$

5. Multiply the number of half-lives by one half-life.

   $$t=2\times 5730=11460$$

6. State the result with units: Estimated age = 11,460 years, under the ideal decay model.

11,460 years