To solve this problem, we need to determine the time it takes for the activity of a radioactive substance to drop to $\frac{1}{16}$ of its initial value.$\\ \\$The half-life of the substance is given as 20 minutes.$\\ \\$The activity of a radioactive substance decreases exponentially over time, and the relationship is given by:$\\ A = A_0 \left(\frac{1}{2}\right)^{\frac{t}{T_{1/2}}} \\$