3. (3 points) Two populations of bacteria evolve continuously in time according to d di CI(t) = -521 (t) + 212(t), 12 (1) = 2ri (t) - 212(t), with initial data (in millions of individuals) = 5, 12(0) = 3. (i) Write the system of ODEs using matrix notation.(ii) Recalling part (iv) of problem 2, compute the explicit solution using formula = F1 (0) :2(t) :T2(0) (iii) Prove that, as time approaches infinity, the population sizes shrink to zero. Namely lim = (1) = lim :2(t) = 0. 1 >| 00