Question

The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a
mastodon had lost 61.1% of their carbon-14. How old were the bones at the time they were discovered?

Answer 1

It would take 7832.4 years for the radioactive element carbon-14 to lose 61.1% of its initial value.

The half life of an element is the time taken for an element to decay to half of its original value. It is given by:

$N(t)=N_o\frac{1}{2}^\frac{t}{t_\frac{1}{2} } \\\\N(t) \ is\ the\ number\ of\ substance\ remaining\ after\ t\ years, N_o\ is \ the\ initial\\value\ t_\frac{1}{2}\ is\ the\ half\ life$

The half life is 5750 years, and it lost 61.1%, hence:

N(t) = 100% - 61.1% = 0.389

$0.389N_o=N_o(\frac{1}{2})^\frac{t}{5750 } \\\\\\0.389=(\frac{1}{2})^\frac{t}{5750 } \\\\\\ln(0.389)=\frac{t}{5750 }ln(0.5)\\\\t=7832.4\ years$

Hence it would take 7832.4 years for the to lose 61.1% of their carbon-14.

Find out more at: https://brainly.com/question/4483570