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Home » Stop Wasting Money: THE Ultimate Guide to Canceling Xbox Game Pass Once and For All! - AMAZONAWS

Stop Wasting Money: THE Ultimate Guide to Canceling Xbox Game Pass Once and For All! - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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📌 f'(u) = \frac{(1 + 9u)^2 \cdot 1 - u \cdot 2(1 + 9u)(9)}{(1 + 9u)^4}.

📌 Simplify numerator:

📌 f'(u) = \frac{(1 + 9u)(1 - 9u)}{(1 + 9u)^4} = \frac{1 - 81u^2}{(1 + 9u)^3}.

📌 Set $ f'(u) = 0 \Rightarrow 1 - 81u^2 = 0 \Rightarrow u^2 = \frac{1}{81} \Rightarrow u = \frac{1}{9} $ (since $ u > 0 $).

📌 Recall $ u = e^{-0.5t} $, so:

📌 e^{-0.5t} = \frac{1}{9} \Rightarrow -0.5t = \ln\left(\frac{1}{9}\right) = -\ln 9 \Rightarrow t = 2\ln 9.

📌 Thus, the time at which the rate of change is maximized is:

📌 Question: A deep-sea microbial population grows such that the number of organisms at time $ t $ is modeled by

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