After sitting on a shelf for a while, a can of soda at a room temperature (73°F) is placed inside a refrigerator and slowly cools. The temperature of the refrigerator is 35°F. Newton's Law of Cooling explains that the temperature of the can of soda will decrease proportionally to the difference between the temperature of the can of soda and the temperature of the refrigerator, as given by the formula below:
After sitting on a shelf for a while, a can of soda at a room temperature (73°F) is placed inside a refrigerator and slowly cools. The temperature of the refrigerator is 35°F. Newton's Law of Cooling explains that the temperature of the can of soda will decrease proportionally to the difference between the temperature of the can of soda and the temperature of the refrigerator, as given by the formula below:
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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![After sitting on a shelf for a while, a can of soda at a room temperature (73°F) is placed inside a refrigerator and slowly cools. The temperature of the refrigerator is 35°F. Newton's Law of Cooling explains that the temperature of the can of soda will decrease proportionally to the difference between the temperature of the can of soda and the temperature of the refrigerator, as given by the formula below:
\[ T = T_a + (T_0 - T_a)e^{-kt} \]
- \( T_a \) = the temperature surrounding the object
- \( T_0 \) = the initial temperature of the object
- \( t \) = the time in minutes](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F607cfd73-341e-40b9-9da6-af1be2ce5002%2F3191f921-f4ca-40c8-be0e-cfc5c185352c%2F3jw1z5f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:After sitting on a shelf for a while, a can of soda at a room temperature (73°F) is placed inside a refrigerator and slowly cools. The temperature of the refrigerator is 35°F. Newton's Law of Cooling explains that the temperature of the can of soda will decrease proportionally to the difference between the temperature of the can of soda and the temperature of the refrigerator, as given by the formula below:
\[ T = T_a + (T_0 - T_a)e^{-kt} \]
- \( T_a \) = the temperature surrounding the object
- \( T_0 \) = the initial temperature of the object
- \( t \) = the time in minutes
![The formula given is:
\[ T = T_a + (T_0 - T_a) e^{-kt} \]
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 problem statement is as follows:
The can of soda reaches the temperature of 53°F after 35 minutes. Using this information, find the value of \( k \), to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the can of soda, to the nearest degree, after 70 minutes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F607cfd73-341e-40b9-9da6-af1be2ce5002%2F3191f921-f4ca-40c8-be0e-cfc5c185352c%2F8ru23yi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The formula given is:
\[ T = T_a + (T_0 - T_a) e^{-kt} \]
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 problem statement is as follows:
The can of soda reaches the temperature of 53°F after 35 minutes. Using this information, find the value of \( k \), to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the can of soda, to the nearest degree, after 70 minutes.
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