Question

Situation:An archaelogist in Turkey discovers aspear head that contains 51% of itsoriginal amount of C-14.N = Noe-ktNo inital amount of C-14 (at timet = 0)N = amount of C-14 at time tk= 0.0001t = time, in yearsFind the age of the spear head to the nearesyear.

Answer 1

Given the formula

$N=N_oe^{-kt}$

Set

$\begin{gathered} N=0.51N_o \\ k=0.0001 \end{gathered}$

And solve for t as shown below

$\begin{gathered} \Rightarrow0.51N_o=N_oe^{-0.0001t} \\ \Rightarrow0.51=e^{-0.0001t} \\ \Rightarrow ln(0.51)=-0.0001tln(e)=-0.0001t \\ \Rightarrow t=\frac{ln(0.51)}{-0.0001} \end{gathered}$

Rounding to the nearest year,

$\Rightarrow t\approx6733$

The answer is 6733 years.