1. Below are tables showing values for two iterated functions. For each function, tell whether it appears to be a chaotic function or not, and why you think so (all of the numbers are percents of the maximum capacity of the environment)

Function A seems to be doing the same sort of thing with both inputs, so it is probably not chaotic; function B is pretty different for the two close inputs (by iteration 16, they are different by 10%), so it looks like it is behaving chaotically.

2. A. Using the population simulation equation

P_n+1 = (1-P_n)*P_n*3+P_n, starting with the value P₀ = .250. Find the first 5 iterations of this function. Does it appear to be staying near a particular value? If so, tell what value it is getting close to.

the first 5 iterations would be: (iteration 0 is .25)

Note: iteration 1 is (1-.25)*.25*3+.25=.8125 which rounds (3 decimal places) to .813

This doesn't seem to be getting close to anything: it is bouncing around in a probably chaotic way.

P_n+1 = (1-P_n)*P_n*2+P_n

This one looks like it is settling down (or possibly bouncing back and forth) to a number between about .9 and 1.09. This one doesn't look as unpredictable as the last one.