# applied algebra

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An artifact was found and tested for its carbon-14 content. If 74% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? Use that carbon-14 has a half-life of 5,730 years.
1 yr

• applied algebra -

the fraction left after t years is

(1/2)^(t/5730)
so, you need to solve for t:
.74 = (1/2)^(t/5730)
ln .74 = t/5730 * ln .5
t = 5730 * ln .74/ln .5
t = 2489, or 2500 years

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