Researchers at Woods Hole Oceanographic Institution have built an iterated matrix model to model orca pop- ulations. They model the population of orca whales using four life stages: yearlings, juveniles, mature adults, and post-reproductive adults: Wn In Un+1 = Mun, with un = yn Zn where un represents the population at time step n, with wn as the number of yearlings, In as the number of juveniles, Un as the number of mature adults, and z, as the number of post-reproductive adults. The time step is 1 year. Suppose that 0 0.01 0.12 0 0.97 0.91 0 0 M = 0 0.07 0.95 0 0 0 0.05 0.982. The matrix M (same matrix from the problem statement on previous page) has the following eigenvalues: X1 = 1.025, A2 = -0.0012, A3 = 0.836, X4 = 0.98, with corresponding eigenvectors: 4 250 36 32 266 469 V1= V. = 30 -20 V3 -288 V4= 34 100 (a) The matrix M is not regular, but the dominant eigenvalue will still determine the long-run behavior of the model. Use the dominant eigenvalue to indicate the long-term growth or decay rate of the orca population. Be sure to state whether the population increases, decreases, or remains constant