My guess is, since this appears to be a programming problem to some extent, that the prof wants you to iterate the update rule (that's what those day-to-day transitions are) to see what happens over many iterations.
This might be more help than one is supposed to give, but here is some Mathematica code for doing this type of iteration.
Clear[f, t]
f[0] = .6;
t[0] = .4;
f[n_] := f[n] = .7*f[n - 1] + .2*t[n - 1]
t[n_] := t[n] = .3*f[n - 1] + .8*t[n - 1]
Now compute f
and t
for some positive integer values of n
, and see what happens.
And stay calm (from your picture, you seem to be beside yourself).