Suppose you have just poured a cup of freshly brewed coffee with temperature 93°C in a room where the temperature is 20ºC. (a) When do you think the coffee cools most quickly? What happens to the rate of cooling as time goes by? Explain. The coffee cools most quickly as soon as ---Select--- ✓. The rate of cooling ---Select--- towards ---Select--- since the coffee approaches room temperature. (b) 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, provided that this difference is not too large. Write a differential equation that expresses Newton's Law of Cooling for this particular situation. (Use t as the independent variable, y as the dependent variable, R as the room temperature, and k as a proportionality constant.) dy dt What is the initial condition? y(0) = In view of your answer to part (a), do you think this differential equation is an appropriate model for cooling? The answer and the model ---Select--- dy ✓ because as y approaches R, approaches ---Select--- dt so the model seems appropriate. (c) Make a rough sketch of the graph of the solution of the initial-value problem in part (b).

Suppose you have just poured a cup of freshly brewed coffee with temperature 93°C in a room where the temperature is 20ºC. (a) When do you think the coffee cools most quickly? What happens to the rate of cooling as time goes by? Explain. The coffee cools most quickly as soon as ---Select--- ✓. The rate of cooling ---Select--- towards ---Select--- since the coffee approaches room temperature. (b) 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, provided that this difference is not too large. Write a differential equation that expresses Newton's Law of Cooling for this particular situation. (Use t as the independent variable, y as the dependent variable, R as the room temperature, and k as a proportionality constant.) dy dt What is the initial condition? y(0) = In view of your answer to part (a), do you think this differential equation is an appropriate model for cooling? The answer and the model ---Select--- dy ✓ because as y approaches R, approaches ---Select--- dt so the model seems appropriate. (c) Make a rough sketch of the graph of the solution of the initial-value problem in part (b).

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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Question

Suppose you poured a cup of freshly brewed coffee with temperature 93 degrees Celsius in a room where the tempature is 20 degrees celsius.

Suppose you have just poured a cup of freshly brewed coffee with temperature 93°C in a room where the temperature is 20°C.
(a) When do you think the coffee cools most quickly? What happens to the rate of cooling as time goes by? Explain.
The coffee cools most quickly as soon as
-Select---
. The rate of cooling ---Select--- ✓ towards -Select---
since the coffee approaches room temperature.
(b) 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, provided that this difference is not too
large. Write a differential equation that expresses Newton's Law of Cooling for this particular situation. (Use t as the independent variable, y as the dependent variable, R as the room temperature,
and k as a proportionality constant.)
dy
dt
What is the initial condition?
y(0)
=
In view of your answer to part (a), do you think this differential equation is an appropriate model for cooling?
The answer and the model --Select---
dy
because as y approaches R, approaches
dt
-Select--- ✓ , so the model seems appropriate.
(c)
Make a rough sketch of the graph of the solution of the initial-value problem in part (b).

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