Question

A farmer in China discovers a mammal hide that contains 68% of its original amount of c-14.

N=n0e^kt


No=amount of c-14 at time t


K=0.0001


T=time in years


Find the age of the mammal hide to the nearest year.

Answer 1

9943

Explanation:

ln0.37/-0.0001 ≈ 9942.522

Answer = 9943

Answer 2

3857 years

Explanation:

The equation is more properly written as ...

`N=N_0e^(-kt) \qquad\text{$N$=amount at time t; $N_0$=initial amount}`

We are only given the ratio N/N0, so we must divide the given formula by N0 to make it work:

`(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=(ln(0.68))/(-0.0001)\approx 3856.6`

The hide is about 3857 years old.