Suppose there is an insect population consisting of two age groups: juveniles and adults. Data shows that each juvenile has 2 offspring (i.e., reproduces at a rate of 200%), while 25% of juveniles mature to become adults. At the same time each adult produces 5 offspring (i.e., reproduces at a rate of 500%, and no adults survive until the next year.

(a) Find the Leslie matrix that models the above insect growth. Please be sure to label your rows and columns.

(b) Find the long-term growth rate or decay of the insect population.

(c) Find the long-term distribution of juveniles and adults as a proportion of the total population.