Answer
41 years.
Work Step by Step
Once the grapes are picked and the wine is made, it doesn’t take in new tritium, which then decays. Calculate the age of the wine using equations 30–4.
$$N=N_0e^{-\lambda t}$$
Now apply equation 30-6, and the given information that the current number of tritium atoms in the wine is only 0.1 times the number with which it started.
$$N=N_0e^{-(ln2)t/(T_{1/2})}=0.10N_0$$
$$0.10=e^{-(ln2)t/(T_{1/2})}$$
Solve for t.
$$t=-\frac{ T_{1/2}ln(0.10)}{ln 2}=-\frac{(12.3y)ln(0.10)}{ln2}=41 y $$
