The size of an undisturbed fish population has been modeled by the formula

Where is the fish population after years and a and b are positive constants that depend on the species and its environment. Suppose that the population in year 0 is Po > 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 lim n†’( 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. Pn+1 a + Pa