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34kurt
2 years ago
6

3. The radioactive element​ carbon-14 has a​ half-life of 5750 years. A scientist determined that the bones from a mastodon had

lost 70.3​% of their​ carbon-14. How old were the bones at the time they were​ discovered?

Mathematics
1 answer:
Lelechka [254]2 years ago
7 0

Answer:

  10,071 years

Step-by-step explanation:

If 'a' is the fraction remaining, it satisfies the equation ...

  a = (1/2)^(t/5750)

Solving for t, we get ...

  log(a) = log(1/2)×t/5750

  t = 5750×log(a)/log(1/2) ≈ -19,101.09×log(a) . . . years

__

If 70.3% is lost, then 1 -0.703 = 0.297 is the fraction remaining. The age is estimated to be ...

  -19,101.09×log(0.297) ≈ 10,071 . . . years

The bones were about 10,071 years old.

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