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Suppose that the rate of change of temperature in a cave in a cool climate is proportional to the difference between the inside temperature, and

Suppose that the rate of change of temperature in a cave in a cool climate is proportional to the difference between the inside temperature, and the current outside temperature, T(t). Assume that there is no heat and that the windows remain closed. The constant of proportionality is k, and time is measured in hours. (a) Derive an initial-value problem

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