Answer:
14734 years
Step-by-step explanation
We know the decay rate with time is given by;
[tex]\frac{dN}{dt}=-kN[/tex]
Where K = 0.0001216 (radioactive decay constant)
Also we know the number of atoms remaining to decay in proportion to original number of atoms is given by;
[tex]Nt=N_{0} e^{-kt}[/tex]
Where,
[tex]N_{0} = N(0)[/tex]
Here we will find [tex]t_{0}[/tex] such that [tex]N(t_{0} )=\frac{1}{6}N_{0}[/tex]
So we can say;
[tex]N(t_{0} )=\frac{1}{6}N_{0}[/tex] ⇔ [tex]N_{0}e^{-kt_{0} } =\frac{1}{6} N_{0}[/tex]
⇒ [tex]e^{-kt_{0} } =\frac{1}{6}[/tex]
Taking natural log on both sides. we get
[tex]ln(e^{-kt_{0} }) = ln (\frac{1}{6} )[/tex]
⇒ [tex]-kt_{0} = ln(1)-ln(6)[/tex]
[tex]-kt_{0} =-1.79175946923[/tex]
[tex]t_{0} = \frac{1.79175946923}{0.0001216} = 14734 (approx)[/tex]
So, the skull is approximately 14734 years old
