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Denote the owl and wood rat populations at time k by Xk = OK RX , where k is in months, OK is the number of owls, and RK 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 = (0.1)OK + (0.5)RK RK + 1 = (-0.18)OK + (1.1)RKA Give a formula for Xk. XK = C1 () + 6 2 As time passes, what happens to the sizes of the owl and wood rat populations? Select the correct choice below and fill in the answer boxes within your choice. (Type whole numbers.) O A. The owl and wood rat populations decline at a rate of owl(s) to thousand rats. B. The owl and wood rat populations grow at a rate of owl(s) to thousand rats. C. The owl and wood rat populations each stabilize in size. Eventually, the populations are in the approximate simplified ratio of owl(s) to thousand rats. Click to select your answer(s).