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Home » \lim_n o \infty b_n = 0 - Sterling Industries

\lim_n o \infty b_n = 0 - Sterling Industries

📅 April 16, 2026 👤 scraface

Apr 16, 2026

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📌 After 14h: 62,500 < 100,000

📌 So after 14 hours, it drops below 100,000.

📌 Each 2 hours halves → decay factor = 0.5 every 2 hours

📌 Set: 8e6 × (0.5)^n < 1e5

📌 Take log: n × log(0.5) < log(0.0125)

📌 n > log(0.0125)/log(0.5) ≈ (-1.903)/(-0.3010) ≈ 6.32 → n ≥ 7 halvings

📌 × 2 = 14 hours

📌 7Dr. Emily Carter identified fossil spores in three sediment layers: upper (18 samples), middle (42), lower (60). She wants to organize them into display cases such that each case has the same number of samples from each layer, with no samples left. What is the maximum number of display cases she can use?

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