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=(ln(0.51))/(-0.0001) \end{gathered}`

Rounding to the nearest year,

`\Rightarrow t\approx6733`

The answer is 6733 years.