How old is a bone which only has 25% of its carbon-14 remaining? The half-life of Carbon-14 is 5,730 years.

Use the formula to solve.

Question

How old is a bone which only has 25% of its carbon-14 remaining? The half-life of Carbon-14 is 5,730 years.

Use the formula   to solve.

BlackTom AI · Accepted Answer

The question asks how old a bone is given that it has 25% of its carbon-14 remaining, with a C-14 half-life of 5730 years.
First, recall that each half-life reduces the quantity by half. 25% corresponds to two half-lives remaining (100% -> 50% -> 25%), so the time elapsed is two half-lives.
Calculate the elapsed time: 2 × 5730 years = 11,460 years.
An alternative approach uses the decay formula N = N0(1/2)^(t/Thalf). If N/N0 = 0.25, then 0.25 = (1/2)^(t/5730). Taking logs, t/5730 = log(0.25)/log(0.5) = 2, so t = 2 × 5730 = 11,460 years.
Note: The provided data set does not include any answer options to select from, so no choice can be picked from a list here. Nevertheless, the calculation shows the bone’s age corresponds to 11,460 years based on the given half-life.

PRECALC141-033 2.8 Practice Problems

How old is a bone which only has 25% of its carbon-14 remaining? The half-life of Carbon-14 is 5,730 years. Use the formula to solve.

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