#OK to post homework
#Nicholas DiMarzio, 09/27/21, Assignment 6
#
#Problem 1
#Using information from first part of problem 1
REC = [0.1, 1.14, 0.04365, 0.082935];
              REC = [0.1, 1.14, 0.873, 0.09]

GrowthCe(REC);
                      1.396724779
#Problem 2
#
G := Matrix([[0.1, 1.2, 0.9, 0.1], [0.95, 0, 0, 0], [0, 0.97, 0, 0], [0, 0, 0.9, 0]]);
                       [0.1   1.2   0.9  0.1]
                       [                    ]
                       [0.95   0     0    0 ]
                  G := [                    ]
                       [ 0    0.97   0    0 ]
                       [                    ]
                       [ 0     0    0.9   0 ]

Eigenvalues(G)[1];
                    1.38573262885364 + 0. I

#Problem 3
#

P := evalf(Matrix([[0.5, 1/6, 1/6, 1/6], [0.2, 0.4, 0.2, 0.2], [7/30, 7/30, 0.3, 7/30], [4/15, 4/15, 4/15, 0.2]]));
      [    0.5       0.1666666667  0.1666666667  0.1666666667]
      [                                                      ]
      [    0.2           0.4           0.2           0.2     ]
 P := [                                                      ]
      [0.2333333333  0.2333333333      0.3       0.2333333333]
      [                                                      ]
      [0.2666666667  0.2666666667  0.2666666667      0.2     ]

P^1000;
 [[0.315197007189532, 0.262664172672962, 0.225140719443162, 

   0.196998129500332], [0.315197007144515, 0.262664172635447, 

   0.225140719411007, 0.196998129472196], [0.315197007112359, 

   0.262664172608651, 0.225140719388038, 0.196998129452099], 

   [0.315197007176892, 0.262664172662428, 0.225140719434133, 

   0.196998129492432]]
#about 31/100 people stay in S1, 26/100 stay in S2, 22/100 stay in S3, and 19/100 stay in S4
#So from this we can see that S1 is the most popular, 
#followed by S2 then S3 then S4 which is the least popular.