Assume that the growth of peacocks obey the rule dP : p³ – 17P² – 38P dt - Here P represents the population of peacocks and t represents the time variable. (a) Find all biologically reasonable equilibrium points. (b) Determine the stability of each biologically reasonable equilibrium. (c) Draw a phase-line diagram. (d) If there are initially 19 peacocks, how many will there be eventually?

Calculus: Early Transcendentals
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Chapter1: Functions And Models
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Assume that the growth of peacocks obey the rule
dP
p3 – 17P² – 38P
dt
Here P represents the population of peacocks and t represents the time variable.
(a) Find all biologically reasonable equilibrium points.
(b) Determine the stability of each biologically reasonable equilibrium.
(c) Draw a phase-line diagram.
(d) If there are initially 19 peacocks, how many will there be eventually?
Transcribed Image Text:Assume that the growth of peacocks obey the rule dP p3 – 17P² – 38P dt Here P represents the population of peacocks and t represents the time variable. (a) Find all biologically reasonable equilibrium points. (b) Determine the stability of each biologically reasonable equilibrium. (c) Draw a phase-line diagram. (d) If there are initially 19 peacocks, how many will there be eventually?
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