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Philip poured himself a boiling hot bowl of soup at 212°F, and left it to stand in a room where the air temperature was 72°F. 6 minutes later the temperature of the soup would be 189°F. To the nearest minute, how many minutes must the soup be left to stand before it reaches a temperature of 152°F?

Philip poured himself a boiling hot bowl of soup at 212°F, and left it to stand in a room where the air temperature was 72°F. 6 minutes later the temperature of the soup would be 189°F. To the nearest minute, how many minutes must the soup be left to stand before it reaches a temperature of 152°F?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem Statement:** Philip poured himself a boiling hot bowl of soup at 212°F and left it to stand in a room where the air temperature was 72°F. Six minutes later, the temperature of the soup would be 189°F. To the nearest minute, how many minutes must the soup be left to stand before it reaches a temperature of 152°F? **Interactive Section:** - **Input your answer:** [Text box] - **Navigation Buttons:** Previous, Submit **Explanation:** This problem involves cooling of an object (the soup) and can be modeled using Newton's Law of Cooling. The law states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature. Here, you can calculate the cooling time to reach the desired temperature using the appropriate formula derived from this law.
Transcribed Image Text:**Problem Statement:** Philip poured himself a boiling hot bowl of soup at 212°F and left it to stand in a room where the air temperature was 72°F. Six minutes later, the temperature of the soup would be 189°F. To the nearest minute, how many minutes must the soup be left to stand before it reaches a temperature of 152°F? **Interactive Section:** - **Input your answer:** [Text box] - **Navigation Buttons:** Previous, Submit **Explanation:** This problem involves cooling of an object (the soup) and can be modeled using Newton's Law of Cooling. The law states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature. Here, you can calculate the cooling time to reach the desired temperature using the appropriate formula derived from this law.
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