Question

Carbon-14 has a half-life of approximately 5,730 years. This exponential decay can be modeled with the function N(t) = N0. If an organism had 200 atoms of carbon-14 at death, how many atoms will be present after 14,325 years? Round the answer to the nearest hundredth.

Answer 1

After 14,325 years, an initial amount of 200 atoms of carbon-14 will decay to approximately 35.4 atoms, using the half-life of 5,730 years and the decay formula N(t) = N0 × (1/2)^(t/t1/2).

Step-by-step explanation:

If an organism had 200 atoms of carbon-14 at death, the number of atoms present after 14,325 years can be calculated using the half-life of carbon-14, which is 5,730 years. To find out how many half-lives have passed, we divide the time elapsed by the half-life: 14,325 years ÷ 5,730 years = 2.5 half-lives.

The decay of carbon-14 can be modeled by the equation N(t) = N0 × (1/2)^(t/t1/2), where N(t) is the number of atoms at time t, N0 is the initial number of atoms, and t1/2 is the half-life of the isotope.

So, the calculation would be:
N(14,325) = 200 × (1/2)^(14,325/5,730)
N(14,325) = 200 × (1/2)^2.5
N(14,325) = 200 × (0.177)
N(14,325) = 35.4

After 14,325 years, there would be approximately 35.4 atoms of carbon-14 left, rounding to the nearest hundredth.