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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 192 °F when freshly poured, and 1 min later has cooled to 182 °F in a room at 70 °F, determine when the coffee reaches a temperature of 144 °F.

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 192 °F when freshly poured, and 1 min later has cooled to 182 °F in a room at 70 °F, determine when the coffee reaches a temperature of 144 °F.

Advanced Engineering Mathematics
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 192 °F when freshly poured, and 1 min later has cooled to 182 °F in a room at 70 °F, determine when the coffee reaches a temperature of 144 °F. Note: Enter the exact symbolic expression for the asked time. The coffee reaches the temperature 144 in In (37) 61 minutes. ✔
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 192 °F when freshly poured, and 1 min later has cooled to 182 °F in a room at 70 °F, determine when the coffee reaches a temperature of 144 °F. Note: Enter the exact symbolic expression for the asked time. The coffee reaches the temperature 144 in In (37) 61 minutes. ✔
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