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Real-World Applicationsmedium
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A server CPU under load generates heat, and its temperature T(t)T(t)T(t) (in ∘C^{\circ}\text{C}∘C) over time ttt (in minutes) follows the model T(t)=75−50e−0.25tT(t) = 75 - 50e^{-0.25t}T(t)=75−50e−0.25t. If the cooling system fails when the temperature exceeds 65∘C65^{\circ}\text{C}65∘C, after how many minutes will the system fail? (Use ln⁡(0.2)≈−1.609\ln(0.2) \approx -1.609ln(0.2)≈−1.609)