In analyzing the battle of Trafalgar in 1805, we saw that if the two forces simply engaged head-on, the British lost the battle and approximately 24 ships, whereas the French Spanish force lost approximately 15 ships. We also saw that Lord Nelson could overcome a superior force by employing a divide-and-conquer strategy. An alternative strategy for overcoming a superior force is to increase the technology employed by the inferior force. Suppose that the British ships were equipped with superior weaponry, and that the FrenchSpanish losses equaled 15% of the number of ships of the opposing force, whereas the British suffered casualties equal to 5% of the opposing force.

a. Formulate a system of difference equations to model the number of ships possessed by each force. Assume the French Spanish force starts with 33 ships and the British start with 27 ships.

b. Build a numerical solution to determine who wins under the new assumption in a head-on engagement.

c. Build a numerical solution for the three battles employing Nelson's divide and conquer strategy coupled with the superior weaponry of the British ships.