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.

Question

Mathematics

Brayden Thompson

1 January, 09:29

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.

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Destiney Clayton · Answer 1

This is of the form f=ir^t. We are given that the half life is 5730 years so we can say:

1=2r^5730

1/2=r^5730 taking natural log of both sides

ln0.5=5730lnr

lnr = (ln0.5) / 5730 raising e to the power of both sides

r=e^ ((ln0.5) / 5730)

r≈0.999879

so we have:

f=200 (0.999879) ^14325

f≈35.34