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 =k(T - A), where T is the temperature of the object after t units of time have passed, A is the ambient 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 62 degrees for 14 minutes, the coffee reaches 170 degrees. How long will it take before the coffee reaches 160 degrees? Include at least 2 decimal places in your answer. dT dt minutes
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 =k(T - A), where T is the temperature of the object after t units of time have passed, A is the ambient 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 62 degrees for 14 minutes, the coffee reaches 170 degrees. How long will it take before the coffee reaches 160 degrees? Include at least 2 decimal places in your answer. dT dt minutes
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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 =k(TA), where T is the temperature of the object after t units of time have passed, A is
dT
dt
the ambient 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 62 degrees for
14 minutes, the coffee reaches 170 degrees. How long will it take before the coffee reaches 160 degrees?
Include at least 2 decimal places in your answer.
minutes
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