rubywombat11Lv1
1 Nov 2021
Problem 14b
Page 499
Section 7.1: Modeling with Differential Equations
Chapter 7: Differential Equations
Textbook ExpertVerified Tutor
1 Nov 2021
Given information
As per the given question
- The room temperature is
and and temperature of coffee is 
.
To find :
- The differential equation that expresses Newton’s law of cooling for the given situation.
- To find the initial condition.
- To answer, do you think this differential equation is an appropriate model for cooling in view of answer to part (a).
Step-by-step explanation
Step 1.
The 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 surrounding, provided that this difference is not too large.
We have to write the differential equation that expresses Newton’s law of cooling for the given situation.
Since temperature of the room temperature is cooler than the temperature of coffee.
Let ,
be the temperature function of coffee.
Single Variable Calculus: Early Transcendentals
4th Edition, 2018
Stewart
ISBN: 9781337687805
Solutions
Chapter
Section
- Problem 1
- Problem 2
- Problem 3a
- Problem 3b
- Problem 4a
- Problem 4b
- Problem 5a
- Problem 5b
- Problem 5c
- Problem 5d
- Problem 6a
- Problem 6b
- Problem 6c
- Problem 6d
- Problem 7a
- Problem 7b
- Problem 7c
- Problem 7d
- Problem 8a
- Problem 8b
- Problem 8c
- Problem 8d
- Problem 9a
- Problem 9b
- Problem 9c
- Problem 10a
- Problem 10b
- Problem 10c
- Problem 11a
- Problem 11b
- Problem 12a
- Problem 12b
- Problem 12c
- Problem 13a
- Problem 13b
- Problem 13c
- Problem 13d
- Problem 14a
- Problem 14b
- Problem 14c
- Problem 15a
- Problem 15b
- Problem 15c