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📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 A seismologist uses AI to predict aftershocks and models the frequency of secondary tremors as inversely proportional to time after the main quake. If there are 48 aftershocks in the first hour, how many are expected in the third hour (assuming proportional decay per hour)?

📌 Since frequency is inversely proportional to time, the number of tremors in hour $ t $ is $ f(t) = \frac{k}{t} $.

📌 But over hour 1: $ f(1) = k/1 = 48 $, so $ k = 48 $.

📌 However, if the model assumes cumulative tremors proportional to $ \sum 1/t $ over discrete hours, then the expected number in hour 3 is proportional to $ 1/3 $.

📌 But if the total tremors up to hour 3 are 48 (integrated), then total = $ k(\frac{1}{1} + \frac{1}{2} + \frac{1}{3}) \approx k(1 + 0.5 + 0.333) = k(1.833) $.

📌 Given 48 in first hour, total up to hour 3 is $ 48 + 24 + 16 + 8 $? Wait — better interpretation: if frequency in hour $ t $ is $ k/t $, and total in hour 1 is $ k/1 = 48 $, so $ k = 48 $.

📌 Then in hour 3, frequency = $ 48/3 = 16 $.

📌 Thus, 16 aftershocks are expected in the third hour.

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