Answer
5.64 half-lives.
Work Step by Step
Use equations 30–5 for the activity.
$$R=R_0e^{-\lambda t}$$
Now apply equation 30-6, and the given information that the current activity is 0.02 times the activity at the beginning.
$$R=R_0e^{-(ln2)t/(T_{1/2})}=0.02R_0$$
$$0.02=e^{-(ln2)t/(T_{1/2})}$$
Solve for the ratio of the elapsed time to the half-life.
$$\frac{t}{T_{1/2}}=-\frac{ln(0.02)}{ln 2}=5.64 $$
You must wait 5.64 half-lives.