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

February 22, 2026

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

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P(t) = P_0 \cdot 2^{t/k}
This expression arises because the publications double every \(k\) years, implying that after \(k\) years, the count is \(2P_0\), after \(2k\) years, it is \(2^2 P_0\), and so on. Thus, the general formula for the number of publications at any time \(t\) is:
To find \(P(2k)\), substitute \(t = 2k\) into the formula:
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:

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