Let r denote the population of rabbits in a geographic region and w the the number of wolves. the respective populations change in time according to the differential equations dr dt = 6r − 2w and dw dt = 2r + w . write the two differential equations as a matrix equation dx/dt = ax, where a is a 2 × 2 matrix and x is a two-component vector. if the initial populations are r(0) = w(0) = 30, what are r(t) and w(t)? after a long time, what is the ratio of rabbits to wolves?