The butterflies on a particular island are not doing too well. Each autumn, every butterfly produces on average 1.2 eggs and then dies. Half of these eggs survive the winter and produce new butterflies by late summer. At this time, 1000 butterflies arrive from the mainland to escape overcrowding.
a. Write a discrete-time dynamical system for the population on this island.
b. Graph the updating function and cobweb starting from 1000.
c. Find the equilibrium number of butterflies.