How many years old is a fossilized tree if it contains 25% of its original carbon-14? (Assume that the half-life of carbon-14 = 5,730 years.)

Question

Quizplus · Accepted Answer

Since carbon-14 has a half-life of 5,730 years, we can use the formula for exponential decay:

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

where A0 is the initial amount, A is the amount after time t, and h is the half-life.

Let's assume the fossilized tree originally had 100% carbon-14. We can use 25% as the amount remaining (A), so:

25 = 100 * (1/2)^(t/5730)

0.25 = (1/2)^(t/5730)

Take the logarithm of both sides:

log(0.25) = (t/5730) * log(1/2)

t = (5730 / log(1/2)) * log(0.25)

t ≈ 11,460 years

Therefore, choice C) 11,460 is the correct answer.

How Many Years Old Is a Fossilized Tree If It