Suppose you have just poured a cup of freshly brewed coffee with temperature 95°C in a room where the temperature is 25°C. Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Therefore, the temperature of the coffee, T(t), satisfies the differential equation =k(T - Troom) where Troom = 25 is the room temperature, and k is some constant. Suppose it is known that the coffee cools at a rate of 2°C per minute when its temperature is 65°C. A. What is the limiting value of the temperature of the coffee? lim T(t) = t-100 B. What is the limiting value of the rate of cooling? dT lim t-100 dt dT dt C. Find the constant k in the differential equation. k
Suppose you have just poured a cup of freshly brewed coffee with temperature 95°C in a room where the temperature is 25°C. Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Therefore, the temperature of the coffee, T(t), satisfies the differential equation =k(T - Troom) where Troom = 25 is the room temperature, and k is some constant. Suppose it is known that the coffee cools at a rate of 2°C per minute when its temperature is 65°C. A. What is the limiting value of the temperature of the coffee? lim T(t) = t-100 B. What is the limiting value of the rate of cooling? dT lim t-100 dt dT dt C. Find the constant k in the differential equation. k
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 59E: According to the solution in Exercise 58 of the differential equation for Newtons law of cooling,...
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