A weak radioactive sample emits decays at an unknown constant rate $n$ per hour. The same detector also registers a known cosmic-ray background at constant rate $b$ per hour, with $b \gg n$. Counts in disjoint time intervals are independent, and the only uncertainty is statistical (Poisson). After observing for $h$ hours, you estimate $n$ by subtracting the known background from the measured total rate. What is the smallest $h$ needed to determine $n$ within a relative uncertainty of $1\%$?