Question 11: The aliens want to inhabit another planet with no resources. They can afford to send one billion aliens with one billion resources (P Ro 1). This time they can equip their space explorers differently, they have two options: 1 and 1. Provide the tools and equipment that correspond to the rates: a = 0.03 and b = 0.0005. Recall that a controls how fast we convert the unallocated resources into population and b controls the rate of growth of knowledge 2. Take less equipment, so a would drop by an order of magnitude, but take more tools that would increase b by an order of magnitude, ie, a = 0.003 and b0.005. If their goal is to maximize the population after 200 years, which option should they take? If they want to maximize the population after 600 years, which option should they take Solve the equations for both scenarios and plot the population P for both cases as function of time on the same plot. Use the rest of the parameters as given below. Make sure you record your responses to the questions in the mark down cell below! H # initial conditions pg 1.0 # billions RO 1.0 # billions # time period Tmax 600 # years H # Put your code here