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.