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Question: a combat model for outcome of a battle suppose two...

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A combat model for outcome of a battle. Suppose two forces, namely B and F, en me, eac that is equal to a fraction a (0,1) of the opposite force. Let Bn and Fn be amount of force of B and F, respectively, at the end of nth unit of time. Then gage in a battle. In each unit of ti h force suffers a loss The use of discrete for the force survived after completely eliminate the opposite force. To improve, assume that a = αΔt where Δt is the time unit. time makes it very difficult to give a formula (a) Convert this model to a continuous time model by letting t → 0. his model is a special case of the Lanchester combat model (b) Given an initial condition B(0)Bo and F(0) - Fo, find the solution to your model. Hint, the general solution to the equation has the following form -AT CkVke where A is an n n matrix with distinct eigenvalues λι, , Xn and the associated eigenvaectors vi, ..., Vn, and C1, ..., Cn are arbitrary constants. (c) Assuming Bo < Fo, find the time T that the force B is completely eliminated. Show that, at that time

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