Show transcribed image text For this worksheet, we continue working with the system of differential equations from the last worksheet describing the population of rabbits and foxes, where R is the population (in hundreds or thousands, for example) of rabbits at any time t, and Fis the population of foxes at any time t (in years). dR dt d+0.8RF One view of solutions for studying solutions to systems of autonomous differential equations is the x-y plane, called the phase plane. The phase plane, which is Gamma's view from the crop duster problem, is the analog to the phase line for a single autonomous differential equation. 1. a.) Use the DE Explorer to plot the solution with initial conditions R-2 and F-3. Sketch the curve below. b.) We can see that the solution, as viewed in the R-F plane, will be a closed curve, but in which direction will the solution go? Clockwise or counterclockwise? Figure this out by completing the table below and then plotting your results with a vector. (Even though you may know the answer from the applet, you should be able to reason about it using the information below.) dR dt dF dt dF dR 2