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Home » You’ll Finally Find the Hidden Village in Minecraft—Here’s the Ultimate Trick! - Decision Point

You’ll Finally Find the Hidden Village in Minecraft—Here’s the Ultimate Trick! - Decision Point

📅 May 6, 2026 👤 scraface

May 06, 2026

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📌 5**Question:** A meteorologist is modeling the temperature changes over a day and defines a function \( T(t) = 3t^2 - 12t + 20 \), where \( T \) is the temperature in degrees Celsius and \( t \) is the time in hours from midnight. Determine the time \( t \) when the temperature reaches its minimum.

📌 To find the time \( t \) when the temperature reaches its minimum, we need to find the vertex of the quadratic function \( T(t) = 3t^2 - 12t + 20 \). The vertex form of a quadratic function \( at^2 + bt + c \) gives the time of minimum (or maximum) as \( t = -\frac{b}{2a} \).

📌 Here, \( a = 3 \) and \( b = -12 \). Thus,

📌 t = -\frac{-12}{2 \times 3} = \frac{12}{6} = 2

📌 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.

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