A forest has a population of wolves and a population of mice. Let x represent the number of wolves (in hundreds) above some level, denoted with 0. So x=−3 corresponds NOT to an absence of wolves, but to a population that is 300 below the designated level of wolves. Similarly, let y represent the number of mice (in hundreds) above a level designated by zero. The following system models the two populations over time: x'=−0.125x+y y'=−x−0.125y Solve the system using the initial conditions x(0)=0 and y(0)=1. x(t) = y(t) = sketch the graph that best represents the solution curve.
A forest has a population of wolves and a population of mice. Let x represent the number of wolves (in hundreds) above some level, denoted with 0. So x=−3 corresponds NOT to an absence of wolves, but to a population that is 300 below the designated level of wolves. Similarly, let y represent the number of mice (in hundreds) above a level designated by zero. The following system models the two populations over time: x'=−0.125x+y y'=−x−0.125y Solve the system using the initial conditions x(0)=0 and y(0)=1. x(t) = y(t) = sketch the graph that best represents the solution curve.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 66EQ
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A forest has a population of wolves and a population of mice. Let x represent the number of wolves (in hundreds) above some level, denoted with 0. So x=−3 corresponds NOT to an absence of wolves, but to a population that is 300 below the designated level of wolves. Similarly, let y represent the number of mice (in hundreds) above a level designated by zero. The following system models the two populations over time:
x'=−0.125x+y
y'=−x−0.125y
Solve the system using the initial conditions x(0)=0 and y(0)=1.
x(t) =
y(t) =
sketch the graph that best represents the solution curve.
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