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

Given

`\begin{gathered} N=(51)/(100)* N_0 \\ \\ N=(51)/(100)* 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=-(0.6733)/(-0.0001) \\ \\ t=6733.44 \\ t=6733 \end{gathered}`