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Home » Macro vs Micro: Which Lens Reveals the Real Stories Behind Market Moves? - Abbey Badges

Macro vs Micro: Which Lens Reveals the Real Stories Behind Market Moves? - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Question:** A historian of science is analyzing the growth of scientific publications over time. If the number of publications doubles every \(k\) years, and the initial count is \(P_0\), express the number of publications \(P(t)\) as a function of time \(t\), and find \(P(2k)\).

📌 Solution:** The problem describes exponential growth. The number of publications at time \(t\) can be modeled by the function:

📌 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:

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

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

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