"The time rate of change of the temperature of an object is proportional to the difference between the temperature surrounding it (called the ambient temperature) and the temperature of the object (which we assume is approximately uniform at all times)" 1. State a differential equation that is a mathematical model of the situation using T to represent temperature of the object, t for time, and k for your constant of proportionality. 2. What is the independent variable? dependent variable? 3. What are the parameters in the model?

"The time rate of change of the temperature of an object is proportional to the difference between the temperature surrounding it (called the ambient temperature) and the temperature of the object (which we assume is approximately uniform at all times)" 1. State a differential equation that is a mathematical model of the situation using T to represent temperature of the object, t for time, and k for your constant of proportionality. 2. What is the independent variable? dependent variable? 3. What are the parameters in the model?

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

"The time rate of change of the temperature of an object is proportional to the difference between the
temperature surounding it (called the ambient temperature) and the temperature of the object (which
we assume is approximately uniform at all times)"
1. State a differential equation that is a mathematical model of the situation using T to represent
temperature of the object, t for time, and k for your constant of proportionality.
2. What is the independent variable?
dependent variable?
3. What are the parameters in the model?

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