24. By suitably renaming the constants and dependent variables in the equations and P' aP(1-aP) I' = rI(S - I) discussed in Section 1.1 in connection with Verhulst's population model and the spread of an epidemic, we can write both in the form y' = ay - by², where a and b are positive constants. Thus, (A) is of the form (C) with y = P, a = a, and b = aa, and (B) is of the form (C) with y = I, a = rS, and b = r. In Chapter 2 we'll encounter equations of the form (C) in other applications.. Choose positive numbers a and b. Construct a direction field and plot some integral curves for (C) in a rectangular region of the form {0 0. Repeat this experiment with various choices of a and b until you can state this property precisely in terms of a and b. Choose positive numbers a and b. Construct a direction field and plot some integral curves for (C) in a rectangular region of the form {0 st≤T, e≤ y ≤0} of the ty-plane. Vary a, b, T and c until you discover a common property of all solutions of (C) with y(0) < 0. (A) (B) (C)
24. By suitably renaming the constants and dependent variables in the equations and P' aP(1-aP) I' = rI(S - I) discussed in Section 1.1 in connection with Verhulst's population model and the spread of an epidemic, we can write both in the form y' = ay - by², where a and b are positive constants. Thus, (A) is of the form (C) with y = P, a = a, and b = aa, and (B) is of the form (C) with y = I, a = rS, and b = r. In Chapter 2 we'll encounter equations of the form (C) in other applications.. Choose positive numbers a and b. Construct a direction field and plot some integral curves for (C) in a rectangular region of the form {0 0. Repeat this experiment with various choices of a and b until you can state this property precisely in terms of a and b. Choose positive numbers a and b. Construct a direction field and plot some integral curves for (C) in a rectangular region of the form {0 st≤T, e≤ y ≤0} of the ty-plane. Vary a, b, T and c until you discover a common property of all solutions of (C) with y(0) < 0. (A) (B) (C)
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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Transcribed Image Text:24. By suitably renaming the constants and dependent variables in the equations
and
P' aP(1-aP)
I' = rI(S - I)
discussed in Section 1.1 in connection with Verhulst's population model and the spread of an epidemic, we can write both in the form
y' = ay - by²,
where a and b are positive constants. Thus, (A) is of the form (C) with y = P, a = a, and b = aa, and (B) is of the form (C) with y = I, a = rS, and b = r. In
Chapter 2 we'll encounter equations of the form (C) in other applications..
Choose positive numbers a and b. Construct a direction field and plot some integral curves for (C) in a rectangular region of the form
{0<t<T, 0≤y≤d}
of the ty-plane. Vary T and d until you discover a common property of all solutions of (C) with y(0) > 0. Repeat this experiment with various choices of a and b
until you can state this property precisely in terms of a and b.
Choose positive numbers a and b. Construct a direction field and plot some integral curves for (C) in a rectangular region of the form
{0 st≤T, e≤ y ≤0}
of the ty-plane. Vary a, b, T and c until you discover a common property of all solutions of (C) with y(0) < 0.
(A)
(B)
(C)
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