After sitting on a shelf for a while, a can of soda at a room temperature (72°F) is placed inside a refrigerator and slowly cools. The temperature of the refrigerator is 39°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 = Ta + (To –- Ta)e-kt Ta the temperature surrounding the object To = the initial temperature of the object

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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After sitting on a shelf for a while, a can of soda at a room temperature (72°F) is
placed inside a refrigerator and slowly cools. The temperature of the refrigerator is
39°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 = Ta + (To – Ta)e-kt
the temperature surrounding the object
To
To = the initial temperature of the object
t = the time in minutes
T = the temperature of the object after t minutes
k = decay constant
The can of soda reaches the temperature of 54°F after 2o 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 100 minutes.
Enter only the final temperature into the input box.
Transcribed Image Text:After sitting on a shelf for a while, a can of soda at a room temperature (72°F) is placed inside a refrigerator and slowly cools. The temperature of the refrigerator is 39°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 = Ta + (To – Ta)e-kt the temperature surrounding the object To To = the initial temperature of the object t = the time in minutes T = the temperature of the object after t minutes k = decay constant The can of soda reaches the temperature of 54°F after 2o 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 100 minutes. Enter only the final temperature into the input box.
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