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Home » oxed{ extThe series converges to rac12} - Moon Smoking

oxed{ extThe series converges to rac12} - Moon Smoking

📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 Using quantum sensing in ecological monitoring, a scientist finds that the growth rate of a rare plant species under controlled stress is modeled by \( P(t) = 2e^{0.3t} \), where \(t\) is time in days. After how many full days will the population first exceed 20 times its initial size?

📌 Initial population at \(t = 0\):

📌 \[ P(0) = 2e^{0} = 2 \]

📌 We want the smallest integer \(t\) such that:

📌 \[ P(t) > 20 \times 2 = 40 \]

📌 2e^{0.3t} > 40

📌 Divide both sides by 2:

📌 e^{0.3t} > 20

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