# An animal dies in the forest. How long will it be until only #7/8# of the original amount of Carbon 14 remains?

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Recall that the half life of Carbon 14 is 5568 years. Round to the nearest year.

*NOTE: The half-life is incorrect. It is 5730 years.*

- Truong-Son

Recall that the half life of Carbon 14 is 5568 years. Round to the nearest year.

*NOTE: The half-life is incorrect. It is 5730 years.
- Truong-Son*

All thanks to Truong-Son Nguyen, aka his method!

We use one of the radioactive decay equation, which states that

Therefore, the decay constant becomes,

And so, we get,

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The half-life of Carbon-14 is approximately 5730 years. Therefore, to determine the time it takes for 7/8 of the original amount of Carbon-14 to remain, we need to find the number of half-lives required. Since 7/8 is equal to 0.875, we need to solve for ( n ) in the equation ( \left(\frac{1}{2}\right)^n = 0.875 ). By taking the logarithm of both sides, we find ( n \approx 3.21 ) half-lives. Multiplying this by the half-life of Carbon-14 (5730 years) yields approximately 18390 years. Therefore, it would take approximately 18390 years for 7/8 of the original amount of Carbon-14 to remain after an animal dies in the forest.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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