A wooden artifact contains 70% Carbon-14. To the nearest year, how many years old is the artifact? The half life of Carbon-14 is 5730 years?

1 answer

We can use the formula for exponential decay to solve this problem:

A = A0 * (1/2)^(t/T)

where A is the amount of Carbon-14 remaining after time t, A0 is the initial amount of Carbon-14, T is the half-life of Carbon-14, and ^(t/T) means "to the power of t divided by T".

We know that the artifact contains 70% Carbon-14, so A/A0 = 0.7. We also know that T = 5730 years. Substituting these values into the formula, we get:

0.7 = 1 * (1/2)^(t/5730)

Taking the natural logarithm of both sides, we get:

ln(0.7) = (t/5730) * ln(1/2)

Solving for t, we get:

t = -5730 * ln(0.7) / ln(1/2)

t ≈ 2,041 years

Therefore, the artifact is approximately 2,041 years old.