(1 point) In a population of a certain uni-sex species, adults give birth to a single juvenile early in the year. Juveniles become reproducing adults in the next year if they survive. Each year 90 percent of the adults give birth to juveniles. Over the year 10 percent of the juveniles survive to become adults. And over the year 80 percent of the adults survive to the next year. Set the problem up as a matrix equation with A₁, as the number of adults at the nth years, J, the number of juveniles at the nth year, and similarly for the n + 1 st year: 0 Jn+1 An+1. 0.1 0.9 0.8 [] Find the eigenvalues of the matrix, smaller one first: A₁ = -0.1 Find corresponding eigenvectors (with 1 as the top entry in each): What happens to the population over time? Extinction Why? Both eigenvalues have absolute value less than 1 A2 0.9 and