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📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Each doubling multiplies the population by 2, so after 6 doublings: 500 × 2⁶ = 500 × 64 = <<500 * 64 = 32000>>32,000 bacteria.

📌 An AI model's accuracy improves by 2.5% each week, starting at 70%. After how many weeks will its accuracy exceed 90%?

📌 We need to solve: 70 × (1.025)^w > 90

📌 Divide both sides by 70: (1.025)^w > 90 / 70 = <<90 / 70 = 1.2857>>1.2857

📌 Take log of both sides: w × log(1.025) > log(1.2857)

📌 w > log(1.2857) / log(1.025) ≈ 0.1096 / 0.0107 ≈ <<0.1096 / 0.0107 ≈ 10.23>>10.23

📌 So w = 11 weeks (smallest integer greater than 10.23).

📌 Two researchers measure the growth of identical plants. Researcher A records growth as 1.2 cm/day starting from 5 cm; Researcher B starts at 3 cm with 1.5 cm/day. After how many days will both plants be the same height?

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