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Use a sketch of the phase line to argue that any solution to the logistic model below, where a, b, and po are positive constants, approaches the equilibrium solution p(t) = as t approaches +∞. a dp dt =(a-bp)p: P(to) - Po First, define the phase line. The phase line for a differential equation The line describes the nature of the equilibrium solutions for f(y) indicates with dots and arrows the of the function dt

Use a sketch of the phase line to argue that any solution to the logistic model below, where a, b, and po are positive constants, approaches the equilibrium solution p(t) = as t approaches +∞. a dp dt =(a-bp)p: P(to) - Po First, define the phase line. The phase line for a differential equation The line describes the nature of the equilibrium solutions for f(y) indicates with dots and arrows the of the function dt

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Use a sketch of the phase line to argue that any solution to the logistic model below, where a, b, and po are positive constants, approaches the equilibrium solution p(t)=ast approaches + ∞o. dp dt = a (a - bp)p: p(to) = Po dy First, define the phase line. The phase line for a differential equation = f(y) indicates with dots and arrows the dt of the function The line describes the nature of the equilibrium solutions for Sketch the phase line for (a bp)p: p (to) Po Choose the correct sketch below. A. P 0 О в. p=0 О с. ○ D. a p=0 10 a p=0 a towards p= and for values of Po such that po > the solution b a How does the phase line indicate that any solution to the logistic model approaches the equilibrium solution p(t) = as t approaches +∞? p=0. a The phase line shows that for values of po such that 0 <po <- the solution towards p=
Transcribed Image Text:Use a sketch of the phase line to argue that any solution to the logistic model below, where a, b, and po are positive constants, approaches the equilibrium solution p(t)=ast approaches + ∞o. dp dt = a (a - bp)p: p(to) = Po dy First, define the phase line. The phase line for a differential equation = f(y) indicates with dots and arrows the dt of the function The line describes the nature of the equilibrium solutions for Sketch the phase line for (a bp)p: p (to) Po Choose the correct sketch below. A. P 0 О в. p=0 О с. ○ D. a p=0 10 a p=0 a towards p= and for values of Po such that po > the solution b a How does the phase line indicate that any solution to the logistic model approaches the equilibrium solution p(t) = as t approaches +∞? p=0. a The phase line shows that for values of po such that 0 <po <- the solution towards p=
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