2. Part II Real World Examples. Pesticides Pesticides that kill all insect species are not only bad for the environment, they can also be inefficient at controlling the pest species and can have unintended consequences. Suppose a pest insect species in a particular field has a population x(t) at a particular time t, and suppose its primary predator is another insect species with population y(t) at time t. Suppose the population of these species are accurately modeled by the system dx = 2.4x 1.2xy dt dy = −y+0.9xy dt Also suppose that at time t = 0 a pesticide is applied to the field that reduces both the pest and predator populations to a very small but non-zero numbers. 1. Use the Slopes app (or other similar app) to investigate what happens to this system. Choose 2 sets of initial conditions, both near zero. Let x(0) = 5y(0). Whatever initial values you choose for your first set, the second set of values should be 1/100 of the first. Plot the solutions. Be sure to expand the scale if necessary, and look out to times 'far' in the future. You will upload these solution curves to GS. You should also try other scenarios to get a feel for what can happen, but you only need to upload 2 graphs. 2. If the pest could be eliminated, would it be eliminated for all time? Explain your answer. Do you think that it is realistic to completely eliminate the pest? 3. If the pest could be eliminated, would it's predator be eliminated for all time too? Explain your answer. 4. Is the behavior of the pest that you found advantageous for the farmers? For the producers of the pesticides?