1. The temperature of a 20lbs Thanksgiving turkey at time t is modeled by a strictly increasing function on the interval [0, 4], twice-differentiable function T(t), where T(t) is measured in degrees Fahrenheit and t is measured in hours. At timet = 0, the temperature of the turkey is 67°F. The turkey is then placed into an oven at 350°F for four hours, beginning at t = 0. Values of T(t) at selected times t for the first 4 hours are given in the table. (a) Use the date in the table to estimate T'(1.5). Show computations that lead to your answer. Using correct units, interpret the meaning of your answer in the context of this problem. 1 (b) For 0
1. The temperature of a 20lbs Thanksgiving turkey at time t is modeled by a strictly increasing function on the interval [0, 4], twice-differentiable function T(t), where T(t) is measured in degrees Fahrenheit and t is measured in hours. At timet = 0, the temperature of the turkey is 67°F. The turkey is then placed into an oven at 350°F for four hours, beginning at t = 0. Values of T(t) at selected times t for the first 4 hours are given in the table. (a) Use the date in the table to estimate T'(1.5). Show computations that lead to your answer. Using correct units, interpret the meaning of your answer in the context of this problem. 1 (b) For 0
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 5T
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Transcribed Image Text:t (hours)
1
3.5
4
T(t) (°F)
67
97.56
122.60 144.80 155.16
165
3.
![1. The temperature of a 20lbs Thanksgiving turkey at time t is modeled by a strictly increasing
function on the interval [0,4], twice-differentiable function T(t), where T(t) is measured in
degrees Fahrenheit and t is measured in hours. At time t = 0, the temperature of the turkey is
67°F. The turkey is then placed into an oven at 350°F for four hours, beginning at t = 0.
Values of T (t) at selected times t for the first 4 hours are given in the table.
(a) Use the date in the table to estimate T'(1.5). Show computations that lead to your answer.
Using correct units, interpret the meaning of your answer in the context of this problem.
(b) For 0 <t < 4, the average temperature of the turkey is - T(t)dt. Use at sum with the 5
1 c4
subintervals indicated by the data in the table to approximate - *T(t)dt. Does this
4
approximation represent an over or under approximation of the average temperature of the
turkey over these 4 hours. Explain your reasoning.
(c) Use the data in the table to evaluate T'(t)dt. Using correct units, interpret the meaning of
ST'(t)dt in the context of the problem.
(d) For t > 4, the turkey is removed from the oven and the function T that models the temperature
of the turkey has first derivative T'(t) = -88.966e¬-847(t-4) Based on this model, what is the
temperature at t = 7?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5ea9b136-d67a-4b38-a71c-ee23174a22b9%2F28cd3a89-707f-42f7-8d03-c5c5689e5443%2F321ankl_processed.png&w=3840&q=75)
Transcribed Image Text:1. The temperature of a 20lbs Thanksgiving turkey at time t is modeled by a strictly increasing
function on the interval [0,4], twice-differentiable function T(t), where T(t) is measured in
degrees Fahrenheit and t is measured in hours. At time t = 0, the temperature of the turkey is
67°F. The turkey is then placed into an oven at 350°F for four hours, beginning at t = 0.
Values of T (t) at selected times t for the first 4 hours are given in the table.
(a) Use the date in the table to estimate T'(1.5). Show computations that lead to your answer.
Using correct units, interpret the meaning of your answer in the context of this problem.
(b) For 0 <t < 4, the average temperature of the turkey is - T(t)dt. Use at sum with the 5
1 c4
subintervals indicated by the data in the table to approximate - *T(t)dt. Does this
4
approximation represent an over or under approximation of the average temperature of the
turkey over these 4 hours. Explain your reasoning.
(c) Use the data in the table to evaluate T'(t)dt. Using correct units, interpret the meaning of
ST'(t)dt in the context of the problem.
(d) For t > 4, the turkey is removed from the oven and the function T that models the temperature
of the turkey has first derivative T'(t) = -88.966e¬-847(t-4) Based on this model, what is the
temperature at t = 7?
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