Solution: The size of an undisturbed fish population has been modeled by the formula
Chapter 11, Problem 93(choose chapter or problem)
The size of an undisturbed fish population has been modeled by the formula where is the fish population after years and and are positive constants that depend on the species and its environment. Suppose that the population in year 0 is . (a) Show that if is convergent, then the only possible values for its limit are 0 and . (b) Show that . (c) Use part (b) to show that if , then ; in other words, the population dies out. (d) Now assume that . Show that if , then is increasing and . Show also that if , then is decreasing and . Deduce that if , then .
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