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Home » Population grows by 12% per generation: \( P = 500 \cdot (1.12)^8 \) - Veritas Home Health

Population grows by 12% per generation: \( P = 500 \cdot (1.12)^8 \) - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 We are given that the clutch size $ n $ satisfies:

📌 n \equiv 1 \pmod{7} \quad \text{and} \quad n \equiv 1 \pmod{11}

📌 This implies:

📌 n - 1 \equiv 0 \pmod{7} \quad \text{and} \quad n - 1 \equiv 0 \pmod{11}

📌 So $ n - 1 $ is a common multiple of 7 and 11. Since 7 and 11 are coprime, their least common multiple is:

📌 \text{lcm}(7, 11) = 7 \cdot 11 = 77

📌 Thus, $ n - 1 = 77k $ for some integer $ k $, and:

📌 n = 77k + 1

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