Newton's Law of Cooling tells us that the rate of change of the temperature of an object is proportional to the temperature difference between the object and its surroundings. This can be modeled by the differential equation dT = k(T – A), where T is the temperature of the object after t units of time have passed, A is the ambient dt temperature of the object's surroundings, and k is a constant of proportionality. Suppose that a cup of coffee begins at 179 degrees and, after sitting in room temperature of 66 degrees for 15 minutes, the coffee reaches 169 degrees. How long will it take before the coffee reaches 156 degrees? Include at least 2 decimal places in your answer.

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Newton's Law of Cooling tells us that the rate of change of the temperature of an object is proportional to the
temperature difference between the object and its surroundings. This can be modeled by the differential equation
dT
= k(T – A), where T is the temperature of the object after t units of time have passed, A is the ambient
dt
temperature of the object's surroundings, and k is a constant of proportionality.
Suppose that a cup of coffee begins at 179 degrees and, after sitting in room temperature of 66 degrees for 15
minutes, the coffee reaches 169 degrees. How long will it take before the coffee reaches 156 degrees?
Include at least 2 decimal places in your answer.
Transcribed Image Text:Newton's Law of Cooling tells us that the rate of change of the temperature of an object is proportional to the temperature difference between the object and its surroundings. This can be modeled by the differential equation dT = k(T – A), where T is the temperature of the object after t units of time have passed, A is the ambient dt temperature of the object's surroundings, and k is a constant of proportionality. Suppose that a cup of coffee begins at 179 degrees and, after sitting in room temperature of 66 degrees for 15 minutes, the coffee reaches 169 degrees. How long will it take before the coffee reaches 156 degrees? Include at least 2 decimal places in your answer.
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