After heating up in a teapot, a cup of hot water is poured at a temperature of 210°F. The cup sits to cool in a room at a temperature of 71°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 Ta =the temperature surrounding the object To = the initial temperature of the object t= the time in minutes %3D T = the temperature of the object after t minutes k= decay constant
After heating up in a teapot, a cup of hot water is poured at a temperature of 210°F. The cup sits to cool in a room at a temperature of 71°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 Ta =the temperature surrounding the object To = the initial temperature of the object t= the time in minutes %3D T = the temperature of the object after t minutes k= decay constant
Chapter6: Exponential And Logarithmic Functions
Section: Chapter Questions
Problem 31PT: A bottle of soda with a temperature of 71 Fahrenheit was taken off a shelf and placed ina...
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Transcribed Image Text:After heating up in a teapot, a cup of hot water is poured at a temperature of
210°F. The cup sits to cool in a room at a temperature of 71°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
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
NC
&
8.
9.
5
Transcribed Image Text:T = the temperature of the object after t minutes
decay constant
The cup of water reaches the temperature of 195°F after 2 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 6 minutes.
Enter only the final temperature into the input box.
Answer:
Submit Answer
attempti out of 2
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4.
7
8.
9.
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5
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