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📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 The minimum temperature occurs at \( t = 2 \) hours from midnight, which is 2 AM. To confirm, we can substitute \( t = 2 \) back into the temperature function:

📌 T(2) = 3(2)^2 - 12(2) + 20 = 12 - 24 + 20 = 8

📌 Thus, the minimum temperature is 8 degrees Celsius at 2 AM.

📌 Question:** An epidemiologist is analyzing the spread of a virus and models the number of infected individuals \( I(t) \) at time \( t \) days with the function \( I(t) = \frac{1000t}{t^2 + 10} \). Find the time \( t \) when the infection rate peaks.

📌 To find the time \( t \) when the infection rate peaks, we need to find the critical points of \( I(t) = \frac{1000t}{t^2 + 10} \) by taking the derivative and setting it to zero.

📌 First, apply the quotient rule for derivatives:

📌 If \( I(t) = \frac{u}{v} \), then \( I'(t) = \frac{u'v - uv'}{v^2} \).

📌 Let \( u = 1000t \), so \( u' = 1000 \);

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