A Scientist determined that the bones from a mastodon had lo

A Scientist determined that the bones from a mastodon had lost 86.2% of their carbon-14. How old were the bones at the time they were discovered?

Solution

Half life of carbon 14 is 5730 yrs

A=A₀(1/2)^t/h

A is the final amount , A₀ is the initial amount , h is the half life

h is the half life

If 86.2% lost, 13.8% left

.138= .862(1/2)^t/5730

.138/862=.5^t/5730

Taking log on both sides

log(138/862)= (t/5730) log.5

log(138/862)/log.5=t/5730

t=5730 log(138/862)/log.5

t=15144.5 yrs