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23. By suitably renaming the constants and dependent variables in the equations and T'=k(T-Tm) G' = -XG+r discussed in Section 1.2 in connection with Newton's law of cooling and absorption of glucose in the body, we can write both as y' = -ay+b, (A) (B) (C) where a is a positive constant and b is an arbitrary constant. Thus, (A) is of the form (C) with y = T, a = k, and b = kT, and (B) is of the form (C) with y = G, a = λ, and b = r. We'll encounter equations of the form (C) in many other applications in Chapter 2. Choose a positive a and an arbitrary b. Construct a direction field and plot some integral curves for (C) in a rectangular region of the form {0≤t≤T, c≤y≤d} of the ty-plane. Vary T, c, and d until you discover a common property of all the solutions of (C). Repeat this experiment with various choices of a and b until you can state this property precisely in terms of a and b.

23. By suitably renaming the constants and dependent variables in the equations and T'=k(T-Tm) G' = -XG+r discussed in Section 1.2 in connection with Newton's law of cooling and absorption of glucose in the body, we can write both as y' = -ay+b, (A) (B) (C) where a is a positive constant and b is an arbitrary constant. Thus, (A) is of the form (C) with y = T, a = k, and b = kT, and (B) is of the form (C) with y = G, a = λ, and b = r. We'll encounter equations of the form (C) in many other applications in Chapter 2. Choose a positive a and an arbitrary b. Construct a direction field and plot some integral curves for (C) in a rectangular region of the form {0≤t≤T, c≤y≤d} of the ty-plane. Vary T, c, and d until you discover a common property of all the solutions of (C). Repeat this experiment with various choices of a and b until you can state this property precisely in terms of a and b.

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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23. By suitably renaming the constants and dependent variables in the equations and T'=k(T-Tm) G' = -XG+r discussed in Section 1.2 in connection with Newton's law of cooling and absorption of glucose in the body, we can write both as y' = -ay+b, (A) (B) (C) where a is a positive constant and b is an arbitrary constant. Thus, (A) is of the form (C) with y = T, a = k, and b = kT, and (B) is of the form (C) with y = G, a = λ, and b = r. We'll encounter equations of the form (C) in many other applications in Chapter 2. Choose a positive a and an arbitrary b. Construct a direction field and plot some integral curves for (C) in a rectangular region of the form {0≤t≤T, c≤y≤d} of the ty-plane. Vary T, c, and d until you discover a common property of all the solutions of (C). Repeat this experiment with various choices of a and b until you can state this property precisely in terms of a and b.
Transcribed Image Text:23. By suitably renaming the constants and dependent variables in the equations and T'=k(T-Tm) G' = -XG+r discussed in Section 1.2 in connection with Newton's law of cooling and absorption of glucose in the body, we can write both as y' = -ay+b, (A) (B) (C) where a is a positive constant and b is an arbitrary constant. Thus, (A) is of the form (C) with y = T, a = k, and b = kT, and (B) is of the form (C) with y = G, a = λ, and b = r. We'll encounter equations of the form (C) in many other applications in Chapter 2. Choose a positive a and an arbitrary b. Construct a direction field and plot some integral curves for (C) in a rectangular region of the form {0≤t≤T, c≤y≤d} of the ty-plane. Vary T, c, and d until you discover a common property of all the solutions of (C). Repeat this experiment with various choices of a and b until you can state this property precisely in terms of a and b.
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