Consider the population example in chapter 7.3. Suppose you have birth rates b1 = 0.3, b2 = 0.3, b3 = 0.3, b4 = 0.1 and death rates d1 = 0.1, d2 = 0.2, d3 = 0.5, d4 = 0.9. (a) What is the biggest eigenvalue of the resulting matrix? What do you expect to happen with the population over a long time period? (b) Suppose you have P1 = 100, P2 = 200, P3 = 150, P4 = 75 in year 0. What will the population be in year 1000? Does this agree with a)? (c) Suppose we change the problem by reducing the death rate d4 = 0.01 of P4 (from 0.9). What is the largest eigenvalue now? What do you expect to happen after a long time period? What is the population after 1000 years?