linear algebra problem?
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?
Comments
matrix:
3/5,3/10
2/5,7/10
two weeks:
453/1000
547/1000
final distribution
3/7= 0.42857142857142855 in field
4/7= 0.5714285714285714 in house