A roast turkey is taken from an oven when its temperature has reached 185°F and is placed on a table in a room where the temperature is 75°F.
(a) If the temperature of the turkey is 150°F after half an hour, what is the temperature after 45 minutes?
(b) When will the turkey have cooled to 100°F?
To find: The temperature after 45 minutes.
The room temperature is .
Newton’s law of cooling:
The formulate Newton’s law of cooling as a differential equation , where k is a constant. The change of variable .
“The only solutions of the differential equation are the exponential functions
Let T be the temperature after the time t.
Substitute in ,
Let and substitute in
Substitute in the above equation,
Since y is a solution of the initial problem with initial condition .
It follows that
Then, the exponential functions .
The temperature of the turkey is after half an hour
To find: The time that is turkey cooled to .
Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!Get Started
Finite Mathematics and Applied Calculus (MindTap Course List)
Precalculus: Mathematics for Calculus (Standalone Book)
Calculus: Early Transcendental Functions
Calculus: An Applied Approach (MindTap Course List)
Single Variable Calculus: Early Transcendentals, Volume I
Essentials Of Statistics
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Calculus (MindTap Course List)
Statistics for The Behavioral Sciences (MindTap Course List)
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Single Variable Calculus
Understanding Basic Statistics
Probability and Statistics for Engineering and the Sciences
Mathematical Excursions (MindTap Course List)
Contemporary Mathematics for Business & Consumers
Elementary Geometry For College Students, 7e
Elementary Technical Mathematics
Mathematical Applications for the Management, Life, and Social Sciences
Single Variable Calculus: Early Transcendentals
Calculus: Early Transcendental Functions (MindTap Course List)
Calculus of a Single Variable
Trigonometry (MindTap Course List)
Elements Of Modern Algebra
Study Guide for Stewart's Multivariable Calculus, 8th
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Finite Mathematics for the Managerial, Life, and Social Sciences
Elementary Geometry for College Students