Solve the following linear system to determine whether the critical point (0,0) is stable, asymptotically stable, or unstable. Use a computer system or graphing calculator to construct a phase portrait and direction field for the give system. Thereby ascertain the stability or instability of each critical point. dx dy dt =y OA. = -25x-6y Find the general solution to the system. Enter the solution as a matrix. x(t) y(t) Choose the phase portrait which matches the system. B. **** 5

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:

Populations of two species are modeled by the equations (equations in picture). Answer the following.    Describe how the species interact with one another. For example, do they compete for the same resources, do they cooperate for mutual benefit, or do they have a predator-prey relationship? Find the equilibrium solutions and explain their significance.

Consider the discrete-time dynamical system modeling the concentration of a chemical in a lung. (Note: round all values at the end of the calculations and use 4 decimal places.)ct+1 = (1-p)ct + pβLet V = 2 L, W = 1 L, and β = 6 mmol/LIf c0 = 7 mmol/L, iterate to find the following values:c1 = ____mmol/Lc2 = ____mmol/Lc3 = ____mmol/Lc4 = ____mmol/LFind the equilibrium of this system:c* = ____mmol/L