An $O(n^{2})$ simulation takes 2 seconds for $n = 1000$ particles. Predict its runtime for $n = 5000$, in seconds.

50 (answers within ±5 count)

$2 \times 25 = 50$ s. Extrapolating by growth class is a superpower: before buying hardware, you know 50,000 particles would take ~83 minutes, and that an $O(n\log n)$ algorithm is worth finding.