We appreciate your visit to After sitting out of a refrigerator for a while a turkey at room temperature 70 degrees F is placed into an oven The oven temperature. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
The value of (k) is approximately (0.060), and after 5.5 hours, the turkey's temperature is around (257°F).
Explanation:
To find the value of ( k ), we can use the given information that the turkey reaches 104 °F after 1.5 hours. Let's use the formula:
104 = 71 + (340 - 71) . e^{-k . 1.5}
Now, solve for ( k ):
33 = 269 . e^{-1.5k}
e^{-1.5k} = {33} / {269}
-1.5k = ln ({33} / {269})
k = -{2} / {3} ln ({33} / {269})
Now that we have the value of ( k ), we can use it to find the temperature after 5.5 hours:
T = 71 + (340 - 71) . e^{-k . 5.5}
Substitute the calculated value of ( k ) into this equation and solve for ( T ). The result will be the Fahrenheit temperature of the turkey after 5.5 hours. Please note that the final temperature should be entered into the input box.
Your complete question is: After sitting out of a refrigerator for a while, a turkey at room temperature (71∘ F) is placed into an oven. The oven temperature is 340∘ F.
Newton's Law of Heating explains that the temperature of the turkey will increase proportionally to the difference between the temperature of the turkey and the temperature of the oven, 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 hours T= the temperature of the object after t hours k= decay constant The turkey reaches the temperature of 104∘ F after 1.5 hours. Using this information, find the value of k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the turkey, to the nearest degree, after 5.5 hours. Enter only the final temperature into the input box.
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