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Consider the differential equation dy -0.5y (y – 4) dt Question 1 Why is the given differential equation considered "autonomous?" The derivative of the unknown function (y) is described only with linear factors such as -0.5y and (y-4), not curves such as sin(y) or 1/y. The derivative of the unknown function (y) is described only in terms of y, not t. The derivative of the unknown function (y) is a first derivative, not a second derivative. Question 2 As a step toward creating a Slope Field graph, complete the table of slope values. Values of y'(t) dy -0.5y (y – 4) dt -1 -2.5 1 1.5 3 1.5 4 -2.5 6

Consider the differential equation dy -0.5y (y – 4) dt Question 1 Why is the given differential equation considered "autonomous?" The derivative of the unknown function (y) is described only with linear factors such as -0.5y and (y-4), not curves such as sin(y) or 1/y. The derivative of the unknown function (y) is described only in terms of y, not t. The derivative of the unknown function (y) is a first derivative, not a second derivative. Question 2 As a step toward creating a Slope Field graph, complete the table of slope values. Values of y'(t) dy -0.5y (y – 4) dt -1 -2.5 1 1.5 3 1.5 4 -2.5 6

Calculus: Early Transcendentals
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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Consider the differential equation dy : -0.5y (y – 4) dt Question 1 Why is the given differential equation considered "autonomous?" The derivative of the unknown function (y) is described only with linear factors such as -0.5y and (y-4), not curves such as sin(y) or 1/y. The derivative of the unknown function (y) is described only in terms of y, not t. The derivative of the unknown function (y) is a first derivative, not a second derivative. Question 2 As a step toward creating a Slope Field graph, complete the table of slope values. Values of y'(t) dy -0.5y (y 4) dt -1 -2.5 1 1.5 3 1.5 4 -2.5
Transcribed Image Text:Consider the differential equation dy : -0.5y (y – 4) dt Question 1 Why is the given differential equation considered "autonomous?" The derivative of the unknown function (y) is described only with linear factors such as -0.5y and (y-4), not curves such as sin(y) or 1/y. The derivative of the unknown function (y) is described only in terms of y, not t. The derivative of the unknown function (y) is a first derivative, not a second derivative. Question 2 As a step toward creating a Slope Field graph, complete the table of slope values. Values of y'(t) dy -0.5y (y 4) dt -1 -2.5 1 1.5 3 1.5 4 -2.5
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