Answer:
The age of the spear head to the nearest year is 1845 years
Step-by-step explanation:
We know that
half life time of C-14 is 5730 years
so, h=5730
we can use formula
[tex]P(t)=P_0(\frac{1}{2})^{\frac{t}{h} }[/tex]
now, we can plug value
[tex]P(t)=P_0(\frac{1}{2})^{\frac{t}{5730} }[/tex]
an archaeologist in turkey discovers a spear head that contains 80% of its original amount of C-14
so,
[tex]P(t)=0.80P_0[/tex]
we can plug it
[tex]0.80P_0=P_0(\frac{1}{2})^{\frac{t}{5730} }[/tex]
now, we can solve for t
[tex]0.80=(\frac{1}{2})^{\frac{t}{5730} }[/tex]
[tex]\ln \left(0.8\right)=\ln \left(\left(\frac{1}{2}\right)^{\frac{t}{5730}}\right)[/tex]
[tex]t=-\frac{5730\ln \left(0.8\right)}{\ln \left(2\right)}[/tex]
[tex]t=1844.647[/tex]
So,
The age of the spear head to the nearest year is 1845 years
