Question

an archaeologist in turkey discovers a spear head that contains 80% of its original amount of C-14. Find the age of the spear head to the nearest year.

Answer 1

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

$P(t)=P_0(\frac{1}{2})^{\frac{t}{h} }$

now, we can plug value

$P(t)=P_0(\frac{1}{2})^{\frac{t}{5730} }$

an archaeologist in turkey discovers a spear head that contains 80% of its original amount of C-14

so,

$P(t)=0.80P_0$

we can plug it

$0.80P_0=P_0(\frac{1}{2})^{\frac{t}{5730} }$

now, we can solve for t

$0.80=(\frac{1}{2})^{\frac{t}{5730} }$

$\ln \left(0.8\right)=\ln \left(\left(\frac{1}{2}\right)^{\frac{t}{5730}}\right)$

$t=-\frac{5730\ln \left(0.8\right)}{\ln \left(2\right)}$

$t=1844.647$

So,

The age of the spear head to the nearest year is 1845 years