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The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon lost 76.1% of their carbon-14. How old were the bones at the time they were discovered?

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asuwafohjames

The bones were 11879.5 years at the time when they were discovered.

What is half-life?

Half-life is the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay

To calculate the years of the bone at the time it was discovered, we use the formula below.

⇒ Formula:

  • R = R'[tex]2^{t/n}[/tex]........... Equation 1

⇒ Where:

  • R = initial Percentage of the bone
  • R' = Percentage of the bone left
  • t = Time
  • n = Half-life

From the question,

⇒ Given:

  • R = 100%
  • R' = 23.9%
  • n = 5750

Substitute into equation 1 and solve for t

  • [tex]2^{n/5750}[/tex] = 100/23.9
  • [tex]2^{n/5750}[/tex] = 4.184
  • n/5750 = log4.184/log2
  • n/5750 = 0.622/0.3010
  • n/5750 = 2.066
  • n = 2.066×5750
  • n = 11879.5 years

The bones were 11879.5 years at the time when they were discovered.

Learn more about half-life here: https://brainly.com/question/25750315

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