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📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 P(2k) = P_0 \cdot 2^{2k/k} = P_0 \cdot 2^2 = 4P_0

📌 Thus, the number of publications after \(2k\) years is:

📌 \boxed{4P_0}

📌 Question:** A deep sea microbiologist is studying the population growth of a chemosynthetic bacterium. The population \(P(t)\) at time \(t\) (in hours) follows the logistic growth model:

📌 P(t) = \frac{1000}{1 + 9e^{-0.5t}}

📌 Find the time \(t\) when the population reaches half of its carrying capacity.

📌 Solution:** The carrying capacity \(K\) of the logistic model is the maximum population, which is 1000 in this case. Half of the carrying capacity is \(500\). We set \(P(t) = 500\) and solve for \(t\):

📌 = \frac{1000}{1 + 9e^{-0.5t}}

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