Question

The radioactive element carbon 14 has a half life of 5750 years. A scientist determined that the bones from a mastodon had lose 75.3% of their carbon 14. How old were the bones at the time they were discovered​

Answer 1

• 11600 years

Explanation:

Given

• Half life = 5750
• Let the initial amount = c
• Final amount = c- 0.753c = 0.247c
• Time = t

The equation

• 0.247c = c(1/2)^(t/5750)
• 0.247 = (1/2)^(t/5750)
• log 0.247 = log (1/2)^(t/5750)
• t/5750 = log 0.247 / log 0.5
• t/ 5750 = 2.017
• t = 5750*2.017
• t = 11600 (rounded)