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📅 July 7, 2026 👤 scraface

Jul 07, 2026

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📌 So the smallest \( n \) is **12**.

📌 An online learning platform observes that course completion rates follow the logistic model \( C(t) = \frac{1000}{1 + 9e^{-0.2t}} \), where \( C(t) \) is the number of completions after \( t \) weeks. After how many weeks does the number of completions first exceed 900?

📌 Solve \( \frac{1000}{1 + 9e^{-0.2t}} > 900 \)

📌 Divide both sides:

📌 \frac{1000}{900} > 1 + 9e^{-0.2t} \Rightarrow \frac{10}{9} > 1 + 9e^{-0.2t}

📌 \frac{10}{9} - 1 > 9e^{-0.2t} \Rightarrow \frac{1}{9} > 9e^{-0.2t}

📌 \frac{1}{81} > e^{-0.2t}

📌 Take natural log:

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