A farmer in China discovers a mammal hide that contains 68% of its original amount of c-14.N=n0e^ktNo=amount of c-14 at time t K=0.0001 T=time in yearsFind the age of the mammal hide to the nearest year.
Accepted Solution
A:
Answer: 3857 yearsStep-by-step explanation:The equation is more properly written as ...[tex]N=N_0e^{-kt} \qquad\text{$N$=amount at time t; $N_0$=initial amount}[/tex]We are only given the ratio N/N0, so we must divide the given formula by N0 to make it work:[tex]\dfrac{N}{N_0}=e^{-kt}\\\\0.68=e^{-0.0001t} \qquad\text{fill in given values}\\\\\ln{0.68}=-0.0001t \qquad\text{take the natural log}\\\\t=\dfrac{\ln{0.68}}{-0.0001}\approx 3856.6[/tex]The hide is about 3857 years old.