A wooden artifact from a dig contains 80% of the carbon-14 that is present in living trees. To the nearest year, about how many years old is the artifact? (The half life of Carbon-14 is 5730 years).
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 in the artifact, A0 is the amount of carbon-14 in living trees, t is the time elapsed, and T is the half-life of carbon-14.
We know that the artifact contains 80% of the carbon-14 in living trees, so:
A = 0.8 * A0
Substituting this into the formula, we get:
0.8 * A0 = A0 * (1/2)^(t/5730)
Dividing both sides by A0, we get:
0.8 = (1/2)^(t/5730)
Taking the natural logarithm of both sides, we get:
ln(0.8) = (t/5730) * ln(1/2)
Solving for t, we get:
t = (5730 / ln(1/2)) * ln(0.8)
t ≈ 3062 years
Therefore, the artifact is about 3062 years old.