We will construct and analyse an age-structured model of a population of plants and seeds. Each plant pro- duces a seeds per year, on average. Each seed has a probability g of germinating in a given year to form a new plant. Seeds that do not germinate within a year are removed from the seed bank. Each plant has a probability d of dying per year. (a) Write down a linear system that describes the population dynamics of plants and seeds from one year to the next. (b) Write your linear system as a matrix equation in the form Ft+1 = Lt. Suppose from now on that each year, every plant produces 100 seeds and has a 25% chance of dying, and that half of seeds germinate. (c) What are the eigenvalues of L? (d) Describe the long-term behaviour of the population (do not calculate the eigenvectors).