Choose oneChoose onean asymptotically stable equilibrium solution.no equilibrium solution at all.an unstable equilibrium solution. dy= f(y).dtThe following problem involves an equation of the formSketch the graph of f(y) versus y, determine the critical (equilibrium)points, and classify each one as asymptotically stable or unstable.Draw the phase line, and sketch several graphs of solutions in thety-plane.dyy(y-2)(y-4), Yo ≥ 0dtThe function y(t) = 0 is[Choose oneThe function y(t) = 2 isChoose oneThe function y(t) = 4 isChoose one=

Given differential equation dydt=y(y-2)(y-4), y0≥0 The objective is to determine the critical…

Answered: = f(y). The following problem involves…

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter6: Rates Of Change

Section6.5: Equations Of Change: Graphical Solutions

Problem 1SBE

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Similar questions

1. The dynamics of a fish population is described by the Richard's growth law dN N (1) dt K where N = N(t) is the population size depending on the continuous time variable 1, and r and K are positive constants.
Sketch a graph of the updating function of the discrete-time dynamical system. Draw a cobwebbing diagram that determines whether the equilibrium point(s) are stable or unstable. (You will want to choose initial conditions near the equilibrium point(s), on each side, to check for stability.) Pt+1 = 0.6Pt + 0.8
Ок Denote the owl and wood rat populations at time k by x = Rk where k is in months, Ok is the number of owls, and R is the number of rats (in thousands). Suppose OK and RK satisfy the equations below. Determine the evolution of the dynamical system. (Give a formula for XK.) As time passes, what happens to the sizes of the owl and wood rat populations? The system tends toward what is sometimes called an unstable equilibrium. What might happen to the system if some aspect of the model (such as birth rates or the predation rate) were to change slightly? Ok+1 = (0.2)0k + (0.5)RK Rk+1=(-0.16)0k + (1.1)Rk Give a formula for xk- xk = 4 ( D +C₂1
Find the equilibrium points and their stability in the system
(2 POINTS) Is it possible for a non-autonomous equation = f(x, y) to have an equilibrium solution y yo (i.e.: constant)? If not, explain. If so, give an example.
Gen solution Identify equilibrium
Consider the autonomous equation: P = 0.05P(100 – P)-h, where P is an animal population, and h is the number of animals harvested per unit time. Determine the values of h which yield no equilibrium states, one equilibrium state, and two equilibrium states. (Your responses should involve equalities or inequalities involving h and a real number.) No equilibrium state: One semi-stable equilibrium state: Two distinct equilibrium states:
Model the situation with a dynamical system. Use your model to answer the question. 12) You take a 259-mg dose of an antibiotic every 5 hours. Your body eliminates 44% of the drug in a 5-hour period. How much antibiotic will be in your bloodstream after two doses? A) Dn+1 = 56Dn + 259, n = 0, 1, 2, .., where Do = 0; 14,763.00 mg B) Dn+1 = 0.56 D n + 259, n = 0, 1, 2, .., where Do = 259; 663.04 mg C) Dn+1 = 0.56D + 259, n = 0, 1, 2, ..., where Do = 0; 404.04 mg %3D %3D %3D %3D %3D %3D %3! D) Dn+1 = 0.44Dn + 259, n = 0, 1, 2, .., where Do = 0; 372.96 mg %3D %3!
Consider the updating function pt+1 = 0.5pt + 4, which measures population after t years.(a) Sketch the graph of the updating function, correctly labeling all axes(b) If p0 = 20, complete the following table to determine the value of p3. t pt pt+1 0 1 2 p3=_______(c) Find the equilibrium point of this system algebraically. You must show the equation you are using to find the equilibrium point, as well as solve the equation
parts B and C
Plot the phaseportrait and characterize the equilibrium.
Ok Denote the owl and wood rat populations at time k by xk = Rk where k is in months, Ok is the number of owls, and R is the number of rats (in thousands). Suppose OK and RK satisfy the equations below. Determine the evolution of the dynamical system. (Give a formula for XK.) As time passes, what happens to the sizes of the owl and wood rat populations? The system tends toward what is sometimes called an unstable equilibrium. What might happen to the system if some aspect of the model (such as birth rates or the predation rate) were to change slightly? Ok+ 1 = (0.4)0k + (0.9)Rk Rk+1=(-0.2)0k +(1.3) Rk

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