Answer
$2.6\times10^4 y$.
Work Step by Step
Once the tree dies, it doesn’t take in new carbon-14, which then decays. Calculate the age of the wooden tool using equation 30–4. and 30–7.
$$N=N_0e^{-\lambda t}$$
Now apply equation 30-6, and the given information that the current number of C-14 atoms is only 4.5 percent of the number with which it started.
$$N=N_0e^{-\lambda t}=N_0e^{-(ln2)t/(T_{1/2})}=0.045N_0$$
Solve for t.
$$t=-\frac{ T_{1/2}ln(0.045)}{ln 2}=-\frac{(5730y)ln(0.045)}{ln2}=2.6\times10^4 y $$
