After sitting out of a refrigerator for a while, a turkey at room temperature (69°F) is placed into an oven. The oven temperature is 300°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: -kt T = Ta + (To – Ta)e¯ Ta = the temperature surrounding the object To = 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 127°F after 3 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 hours. Enter only the final temperature into the input box.

After sitting out of a refrigerator for a while, a turkey at room temperature (69°F) is placed into an oven. The oven temperature is 300°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: -kt T = Ta + (To – Ta)e¯ Ta = the temperature surrounding the object To = 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 127°F after 3 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 hours. Enter only the final temperature into the input box.

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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Question

**Understanding Newton's Law of Heating and Cooling**

After sitting out of a refrigerator for a while, a turkey at room temperature (69°F) is placed into an oven. The oven temperature is 300°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:

\[ T = T_a + (T_0 - T_a)e^{-kt} \]

Where:
- $ 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

Given:
- The turkey reaches the temperature of 127°F after 3 hours.

### Problem
1. **Find the value of $ k $** to the nearest thousandth.
2. **Determine the Fahrenheit temperature of the turkey** to the nearest degree, after 5 hours using the resulting equation.

### Instructions
- Enter only the final temperature into the input box.

By understanding and applying Newton's Law of Heating, you'll be able to predict how the temperature of the turkey changes over time when exposed to a constant high temperature, such as in an oven.

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