After heating up in a teapot, a cup of hot water is poured at a temperature of 204°F. The cup sits to cool in a room at a temperature of 67°F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between the temperature of the water and the temperature of the room, as given by the formula below: T = Ta+ (To – Ta)e kt %3D Ta = the temperature surrounding the object To =the initial temperature of the object t= the time in minutes T=the temperature of the object after t minutes k = decay constant %3D %3D The cup of water reaches the temperature of 181°F after 3 minutes. Using this information, find the value of k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 5 minutes. Enter only the final temperature into the input box.
After heating up in a teapot, a cup of hot water is poured at a temperature of 204°F. The cup sits to cool in a room at a temperature of 67°F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between the temperature of the water and the temperature of the room, as given by the formula below: T = Ta+ (To – Ta)e kt %3D Ta = the temperature surrounding the object To =the initial temperature of the object t= the time in minutes T=the temperature of the object after t minutes k = decay constant %3D %3D The cup of water reaches the temperature of 181°F after 3 minutes. Using this information, find the value of k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 5 minutes. Enter only the final temperature into the input box.
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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![**Newton's Law of Cooling: Educational Overview**
After heating up in a teapot, a cup of hot water is poured at a temperature of 204°F. The cup sits to cool in a room at a temperature of 67°F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between the temperature of the water and the temperature of the room, as given by the formula below:
\[ T = T_a + (T_0 - T_a)e^{-kt} \]
Where:
- \( T_a \) = the temperature surrounding the object
- \( T_0 \) = the initial temperature of the object
- \( t \) = the time in minutes
- \( T \) = the temperature of the object after \( t \) minutes
- \( k \) = decay constant
The cup of water reaches the temperature of 181°F after 3 minutes. Using this information, find the value of \( k \), to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 5 minutes.
Enter only the final temperature into the input box.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F607cfd73-341e-40b9-9da6-af1be2ce5002%2F57d185e3-b95e-41a6-9fb3-ae7586340348%2F24k8ppr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Newton's Law of Cooling: Educational Overview**
After heating up in a teapot, a cup of hot water is poured at a temperature of 204°F. The cup sits to cool in a room at a temperature of 67°F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between the temperature of the water and the temperature of the room, as given by the formula below:
\[ T = T_a + (T_0 - T_a)e^{-kt} \]
Where:
- \( T_a \) = the temperature surrounding the object
- \( T_0 \) = the initial temperature of the object
- \( t \) = the time in minutes
- \( T \) = the temperature of the object after \( t \) minutes
- \( k \) = decay constant
The cup of water reaches the temperature of 181°F after 3 minutes. Using this information, find the value of \( k \), to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 5 minutes.
Enter only the final temperature into the input box.
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