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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

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.EA: Extended Application Managing Renewable Resources
Problem 1EA: Suppose that a particular plot of land can sustain 500 deer and that the population of this...
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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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