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The temperature T of a body will increase or decrease at a rate proportional to the...

The temperature T of a body will increase or decrease at a rate proportional to the temperature difference respectively below or above the surrounding temperature, T¯, the constant of proportionality being k. Derive an expression depicting the temperature of the body as a function of the time given that its initial temperature is T0. Sketch, by inspection, the graph of T = T(t) when T0 < T¯, and when T0 > T¯.

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