1.3 Continuous Time Simulation [15 points] Consider a population model for wolves and sheep, species in a predator-prey relationship where each population increases by a birth rate and decreases by a death rate, represented here by a System Dynamics model. Wolf Population Wolf Births Wolf Deaths Sheep Population Sheep Births Sheep Deaths In this model, the flow equations (birth and death rates) take the form: WolfBirths = 0.002 * Wolf Population * SheepPopulation Wolf Deaths = 0.4 * Wolf Population SheepBirths = 0.05 * SheepPopulation SheepDeaths = 0.025 * Wolf Population * SheepPopulation (a) 5 PTS Write the differential equations for the state variables Wolf Popul W(t) and SheepPopulation S(t) based on the in-flows and out-flow above: dW 1 dt d.S dt (b) 5 PTS Write the state transition for W(t) and S(t) using Euler's gration method: 8(W) = W(t + At) = 6(S) = S(t + At) = (c) 5 PTS Perform a manual simulati