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Home » Solution: Use partial fractions to decompose $ \frac1k(k+1)(k+2) $. Let: - Dachbleche24

Solution: Use partial fractions to decompose $ \frac1k(k+1)(k+2) $. Let: - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 With rotation: \( 2.5 + 3 \times 0.3 = 2.5 + 0.9 = 3.4\% \)

📌 Continuous decline: \( 2.5 - 3 \times 0.1 = 2.5 - 0.3 = 2.2\% \)

📌 Difference = 3.4 - 2.2 = 1.2%

📌 The marine biologist observes that a new coral variant doubles in colony size every 18 months. Starting with a 5 cm² colony, what will its area be (in cm², to the nearest whole) after 4.5 years?

📌 years = 54 months → \( 54 / 18 = 3 \) doubling periods.

📌 Final size = \( 5 \times 2^3 = 5 \times 8 = 40 \) cm²

📌 A healthcare analyst models patient wait times: with a new scheduling system, wait times drop by 20% in emergency departments. If the original average wait was 50 minutes, and a patient arrives immediately after a 50-minute wait, how many minutes shorter is the new wait, and what is the new wait time?

📌 Drop = \( 0.2 \times 50 = 10 \) minutes

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