Question: The size of an undisturbed fish population
The size of an undisturbed fish population has been modeled by the formula where Pn is the fish population after n years and a and b are
positive constants that depend on the species and its environment. Suppose that the population in year 0 is p0 > 0.
(a). Show that if {pn} is convergent, then the only possible values for its limit are 0 and b - a.
(b). Show that Pn+1 (c). Use part (b) to show that if a > b, then limn→∞ Pn = 0; in other words, the population dies out.
(d). Now assume that a b -a, then {Pn} is decreasing and Pn > b - a.
Deduce that if a
Transcribed Image Text:
bp. Pa+1 a + Pa
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