Question 3: In a forest in Alberta, every year 20% of the population of red deer either die of natural causes or are eaten by predators. In the meantime, there are 1000 new red deer. The discrete-time dynamical system that gives the population of red deer each year is pt+1 = 0.8pt + 1000. (a) If there are 2000 red deer now, how many red deer will be there three years later? (b) Give the updating function of the dynamical system. Find its inverse, if it exists. (c) Determine all equilibrium points of the dynamical system, and of its inverse. (d) Find the general solution of the dynamical system (ie., a formula in terms of t) given the initial condition p0 = 2000.
Question 3: In a forest in Alberta, every year 20% of the population of red deer either die of natural causes or are eaten by predators. In the meantime, there are 1000 new red deer. The discrete-time dynamical system that gives the population of red deer each year is pt+1 = 0.8pt + 1000. (a) If there are 2000 red deer now, how many red deer will be there three years later? (b) Give the updating function of the dynamical system. Find its inverse, if it exists. (c) Determine all equilibrium points of the dynamical system, and of its inverse. (d) Find the general solution of the dynamical system (ie., a formula in terms of t) given the initial condition p0 = 2000.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question 3: In a forest in Alberta, every year 20% of the population of red deer either die of natural causes or are eaten by predators. In the meantime, there are 1000 new red deer. The discrete-time dynamical system that gives the population of red deer each year is pt+1 = 0.8pt + 1000.
(a) If there are 2000 red deer now, how many red deer will be there three years later?
(b) Give the updating function of the dynamical system. Find its inverse, if it exists.
(c) Determine all equilibrium points of the dynamical system, and of its inverse.
(d) Find the general solution of the dynamical system (ie., a formula in terms of t) given the initial condition p0 = 2000.
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