Question: If C = 100, k = 0.1, and t is time in minutes, how long will it take a hot cup of coffee to cool

If C = 100, k = 0.1, and t is time in minutes, how long will it take a hot cup of coffee to cool to a temperature of 25°C in a room at 20°C?

Newton’s law of cooling says that the rate at which a body cools is proportional to the difference in temperature between the body and an environment into which it is introduced. This leads to an equation where the temperature ƒ(t ) of the body at time t after being introduced into an environment having constant temperature T0 is ƒ(t) = T₀ + Ce^-kt, where C and k are constants.

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