Question

Situation:A hiker in Africa discovers a skull thatcontains 51% of its original 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 skull to the nearest year

Answer 1

Solution

Given

$\begin{gathered} N=\frac{51}{100}\times N_0 \\ \\ N=\frac{51}{100}\times N_0 \\ \\ N=0.51N_0 \\ \\ \end{gathered}$$\begin{gathered} N=N_0e^{-kt} \\ \\ 0.51N_0=N_0e^{-0.0001t} \\ \\ 0.51=e^{-0.0001t} \end{gathered}$

Solve for t using natural logarithm

$\begin{gathered} \log_e0.51=-0.0001t \\ -0.6733=-0.0001t \\ t=-\frac{0.6733}{-0.0001} \\ \\ t=6733.44 \\ t=6733 \end{gathered}$