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# The size of an undisturbed fish population has been modeled by the formula pn11 bpn a 1

ISBN: 9781305270336 484

## Solution for problem 93 Chapter 11.1

Single Variable Calculus: Early Transcendentals | 8th Edition

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Problem 93

The size of an undisturbed fish population has been modeled by the formula pn11 bpn a 1 pn 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 h pnj is convergent, then the only possible values for its limit are 0 and b 2 a. (b) Show that pn11 , sbyadpn. (c) Use part (b) to show that if a . b, then limnl pn 0; in other words, the population dies out. (d) Now assume that a , b. Show that if p0 , b 2 a, then h pnj is increasing and 0 , pn , b 2 a. Show also that if p0 . b 2 a, then h pnj is decreasing and pn . b 2 a. Deduce that if a , b, then limnl pn b 2 a.

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Ways of Knowing & Approaches to Research -Lecture: Everyday ways of knowing (authority, experience, etc.) & their problems; characteristics of science; goals of science; research approaches (science/positivism vs interpretive vs. critical); induction & deduction; quantitative & qualitative methods; basic/theoretical/scholarly research vs. applied -Ch. 1 & Ch. 2: lecture overlap, plus proprietary research (Ch. 2); additional info/terms in some overlap areas. Text Ch. 3: there is some “testable” info t (e.g., primary vs. secondary sources; peer review; etc.) Lecture: Review Lectures 2 & 3 Chapter 1 What is research  Research: the activity of conducting intellectual investigations into the observable world o Social research: focuses less on the observable world in which human beings interact and more on the interactions themselves, how they come into existence, how they function, and how they affect the human experience How do we know what we know  Epistemology: the study of knowledge o Experience: a common way of understanding the social world through previous experiences ("learning the hard way") o Tenacity: the assumption that something is true because it has always been said to be true (norms and assumptions) o Authority: the reliance upon someone in a position of power to determine what is factual; may be derived from a variety of places (political power, religious authority, interpersonal trust)

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