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

Solution

Given that;

$\begin{gathered} N=N_0e^{-kt} \\ \\ \text{ Given that } \\ \\ N=\frac{42}{100}N_0 \\ \\ k=0.0001 \end{gathered}$

we need to find t,

=>

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

The answer is 8675 years