The Lanchester combat equations , developed by the British mathematician Frederick W. Lanchester during World War I to analyze the new phenomenon of aerial warfare, consider the levels x ( t ) and y ( t ) of two opposing forces at time t , and how these levels are depleted. The modern Lanchester equations are dx / dt 5 2a y ( t ) dy / dt 5 2b x ( t ) where a and b are positive attrition coeff cients. These state that the rate of depletion of each force is proportional to the size of the other force. For a 5 b 5 0.01 and initial force levels x (0) 5 1000 and y (0) 5 500, create an Arena model that will run until one side or the other is completely depleted, that is, until x ( t ) 5 0 or y ( t ) 5 0, whichever comes f rst. At what time does this happen? Include a plot of both force levels, as well as Variable animations of them, and a Variable animation of the current time. Use Base Time Units of Hours. Note that analytical solutions to these differential equations can be developed, making simulation unnecessary. (Thanks to Professor Tom Lucas of the Naval Postgraduate School for motivating this and the next three Exercises, as well as for the numerical values of the constants and starting boundary conditions.)