I need help with this multiple part question and please explain each part please because I get easily confused.

(4) A colony of Carpenter ants inhabit two nearby mounds. There are at ants on the rst mound and bt ants on the second mound. Each day, 15% of the ants from the rst mound travel to the second, and 25% of the ants from the second mound travel to the rst. Let rt be the proportion of ants on the second mound. You can verify the updating function for this system is n+1=.15(1 n) + .75rt. (a) Notice the updating function is a weighted average. Interpret the meaning with sen- tences that start with the following prompts: a The weights are... a If the weight is large, the model emphasizes . This makes biological sense because... (b) Find the equilibrium point(s) of the system for rt algebraically. Now suppose that of those ants traveling from mound 1 to mound 2, 10% die before making it to mound 2. You can verify that the new updating function for T; is .135 + .615rt .985 + 015?"? (c) Do you expect the equilibria in this new model to be smaller or larger than the equilibria from (b)? Why? Do you expect the equilibrium point to be stable or unstable? Why? Hint: Pick a few different initial conditions and iterate the updating function several times. (d) Find the new equilibrium point for this system algebraically. Tt+1 Z