Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. If the coffee has a temperature of 172 °F when freshly poured, and 1 min later has cooled to 162 °F in a room at 70 °F, determine when the coffee reaches a temperature of 129 °F. Note: Enter the exact symbolic expression for the asked time. The coffee reaches the temperature 129 in minutes.
Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. If the coffee has a temperature of 172 °F when freshly poured, and 1 min later has cooled to 162 °F in a room at 70 °F, determine when the coffee reaches a temperature of 129 °F. Note: Enter the exact symbolic expression for the asked time. The coffee reaches the temperature 129 in 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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![Newton's law of cooling states that the temperature of an object
changes at a rate proportional to the difference between its
temperature and that of its surroundings. Suppose that the
temperature of a cup of coffee obeys Newton's law of cooling. If the
coffee has a temperature of 172 °F when freshly poured, and 1 min
later has cooled to 162 °F in a room at 70 °F, determine when the
coffee reaches a temperature of 129 °F.
Note: Enter the exact symbolic expression for the asked time.
The coffee reaches the temperature 129 in
minutes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc373888-a70a-4c0e-9c9b-f21d80fbbf5a%2Fe9f4f542-d2f9-4ff6-b4c8-688960b8cf2e%2Fqxeqo3x_processed.png&w=3840&q=75)
Transcribed Image Text:Newton's law of cooling states that the temperature of an object
changes at a rate proportional to the difference between its
temperature and that of its surroundings. Suppose that the
temperature of a cup of coffee obeys Newton's law of cooling. If the
coffee has a temperature of 172 °F when freshly poured, and 1 min
later has cooled to 162 °F in a room at 70 °F, determine when the
coffee reaches a temperature of 129 °F.
Note: Enter the exact symbolic expression for the asked time.
The coffee reaches the temperature 129 in
minutes.
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