Just write what you are doing in matrix form
The population of rats in my farm moves constantly back and forth between the house and the field. Every week 40% of the rats in the field move to my house while 30% of those in my house move to the field. Suppose that, initially, the distribution of this population is: 70% in the field and 30% in my house.
(a) Find the migration matrix and set up a difference equation for this situation.
(b) What is the rats’ distribution after two week in my farm?
a) I get this migration matrix:
0.70 0.40
0.30 0.60
Is this correct? If so, how do I set up a difference equation?
b)
0.70 0.40
0.30 0.60
multiply this matrix by:
0.70
0.30
this will give the rats distribution after 1 week, and multiply by that again to get the distribution after two weeks. Is this correct?
Please can someone give me some guidance on this problem.