Question

The radioactive element carbon 14 has a hall of 5750 years. A scientist determined that the bones from a mastodon had lost 70.8% of their carbon14. How old were the bones at the time they were discovered The bones were about years old (Round to the nearest Integer as needed

Answer 1

$A=P\left(0.5\right)^{\frac{t}{p}}$

here A=0.292P

and the half-life is p=5750 years

$0.292P=P\left(0.5\right)^{\frac{t}{5750}}$

$0.292=\left(0.5\right)^{\frac{t}{5750}}$

$\ln \left(0.292\right)=\ln \left(0.5^{\frac{t}{5750}}\right)$

In (0.292) t In (0.5) 5750

$5750\ln \left(0.292\right)=t\ln \left(0.5\right)$

$\frac{5750\ln \left(0.292\right)}{\ln \left(0.5\right)}=t$

$t=\frac{5750\ln \left(0.292\right)}{\ln \left(0.5\right)}$

$t \approx {\color{Red} 10212}$

.

the bones were about 10212 years old