The academics and the technicians of a university faculty are planning a paintball battle and the mathematicians are trying to predict their chances of winning with a continuous model. They are representing the numbers in the two teams at any time t as and respectively and have decided that the system to model the encounter should be dA/dT= - k2T and dT/dt= - K1A, where k1 and k2 are positive constants. Based on the initial conditions A(0)=100, T(0)=80, The system of ODEs can of course be solved analytically using eigenvalue techniques of the populations over a 20 minutes battle. = By using the separation of variables, then integrating bothe sides of dA/dT=-k2t i got A=-k2Tt + c1, where c1 is constant. At initial , A=100, A=c1= 100, therefore i got A=-k2Tt + 100. Similary for dT/dt= - K1A, I got T=-k1At + 80 Can some one help after that to solve the systems of ODEs. ADDITIONAL QS FOR THE ABOVE SOLUTION. YOU CAN IGNORE MAPLE BIT FROM b) but does it have something to do with the above solution ans part c). TO solve part c, do i have to use part b) qs part. THE ABOVE SOLUTION I HAVE DONE IS FOR PART C BUT ITS STILL INCOMPLETE AND NOT SURE WITH ANSWER TOO PLEASE HELP. CONTINUE QS b)The muscles and eyesight of the academics have of course suffered from too much ‘book learning’ over the years, but at least they are aware of their limitations as good soldiers. They estimate that although both sides can fire paintballs at the same rate as each other, denoted by f_A =f_T =2 shots per minute, the technicians have a probability of 0.035 of hitting their target with a single paintball shot whilst the academics have only a 0.01 probability of hitting theirs. Based on the initial conditions A(0)=100, T(0)=80, use Maple to produce a numerical approximation and graph of the populations over a 20 minutes battle then comment on the outcome after that time. (c)The system of ODEs can of course be solved analytically using eigenvalue techniques. Do this and compare it with predicted team numbers remaining standing after 20 minutes from your Maple simulation to ensure correctness.