According to Newton′s Law of Cooling, the rate of change of an object's temperature is proportional to the difference between the temperature of the the object and that of the surrounding medium. The accompanying figure shows the graph of the temperature T (in degrees Fahrenheit) versus time t (in minutes) for a cup of coffee, with initial temperature 200 degrees Fahrenheit, that is allowed to cool in a room with a constant temperature of 75 degrees Fahrenheit.
According to Newton′s Law of Cooling, the rate of change of an object's temperature is proportional to the difference between the temperature of the the object and that of the surrounding medium. The accompanying figure shows the graph of the temperature T (in degrees Fahrenheit) versus time t (in minutes) for a cup of coffee, with initial temperature 200 degrees Fahrenheit, that is allowed to cool in a room with a constant temperature of 75 degrees Fahrenheit.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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According to Newton′s Law of Cooling, the rate of change of an object's temperature is proportional to the difference between the temperature of the the object and that of the surrounding medium. The accompanying figure shows the graph of the temperature T (in degrees Fahrenheit) versus time t (in minutes) for a cup of coffee, with initial temperature 200 degrees Fahrenheit, that is allowed to cool in a room with a constant temperature of 75 degrees Fahrenheit.
Transcribed Image Text:(a) Estimate T when t = 10 minutes:
(b) Estimate dT/dt when t = 10 minutes:
Newton's Law of Cooling can be expressed as "
k(T – To) ,where k is the constant of proportionality and
-
dt
T, is the temperature of the surrounding medium.
(c) Use the results of parts (a) and (b) to estimate the value of k.
Value of k:
Transcribed Image Text:200
10.0
5,0
10
60
-10
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