Question

Situation:A farmer in China discovers a mammalhide that contains 42% of its originalamount of C-14.N = Noe-ktNoinital amount of C-14 (at timet = 0)N= amount of C-14 at time tk= 0.0001t = time, in yearsFind the age of the mammal hide to the nearestyear.

Answer 1

Given that;

`\begin{gathered} N=N_0e^(-kt) \\ \\ \text{ Given that } \\ \\ N=(42)/(100)N_0 \\ \\ k=0.0001 \end{gathered}`

we need to find t,

=>

`\begin{gathered} (42)/(100)N_0=N_0e^(-0.0001t) \\ \\ \Rightarrow(42)/(100)=e^(-0.0001t) \\ \\ \Rightarrow\ln((42)/(100))=-0.0001t \\ \\ \Rightarrow t=(\ln((42)/(100)))/(-0.0001) \\ \\ \Rightarrow t=8675 \end{gathered}`

The answer is 8675 years