Question

Prehistoric cave paintings were discovered in a cave in France. The paint contained 38% of the original carbon-14. Use the exponential decay model for carbon-14

A=A0e^-0.0001211, to estimate the age of the paintings.

The paintings are approximately years old. (Round to the nearest integer.)

Answer 1

Explanation:

To solve this problem, we need to first determine the half-life of carbon-14. Using the given decay model, we can see that the rate of decay, or the decay constant, is 0.0001211. The half-life, t1/2, is therefore ln(2)/0.0001211 = 5,730 years. We can then solve for the age of the paintings using the formula t = ln(2) / ln(A/A0). In this case, A/A0 = 0.38. So, t = ln(2)