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 dT 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 temperature of the object's surroundings, and k is a constant of proportionality. Suppose that a cup of coffee begins at 188 degrees and, after sitting in room temperature of 68 degrees for 18 minutes, the coffee reaches 178 degrees. How long will it take before the coffee reaches 166 degrees? Include at least 2 decimal places in your answer. 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 dT 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 temperature of the object's surroundings, and k is a constant of proportionality. Suppose that a cup of coffee begins at 188 degrees and, after sitting in room temperature of 68 degrees for 18 minutes, the coffee reaches 178 degrees. How long will it take before the coffee reaches 166 degrees? Include at least 2 decimal places in your answer. minutes
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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(T – A), where T is the temperature of the object after t units of time
dt
dT
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 188 degrees and, after sitting in room temperature of 68 degrees
for 18 minutes, the coffee reaches 178 degrees. How long will it take before the coffee reaches 166
degrees?
Include at least 2 decimal places in your answer.
minutes
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