Homework 11 Solutions - 16 April 2015 Math 110 Spring 2015...

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16 April 2015 Math 110 Spring 2015 week 11 homework solutions 5.3.6 A hospital trauma unit has determined that 30% of its patients are ambulatory and 70% are bedridden at the time of arrival at the hospital. A month after arrival, 60% of the ambulatory patients have recovered, 20% remain ambulatory, and 20% have become bedridden. After the same amount of time, 10% of the bedridden patients have recovered, 20% have become ambulatory, 50% remain bedridden, and 20% have died. Determine the percentages of patients who have recovered, are ambulatory, are bedridden, and have died 1 month after arrival. Also determine the eventual percentages of patients of each type.
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16 April 2015 Now we compute how to write x 0 as a linear combination of these four eigenvectors. Forming the matrix Q whose columns are the four eigenvectors, we solve Qc = x 0 = 1 0 2 - 5 . 5 0 0 - 1 9 0 0 - 2 - 4 . 5 0 1 1 1 c = 0 0 . 3 0 . 7 0 . Performing a row-reduction yields c = 59 / 90 31 / 90 - 0 . 34 - 4 / 900 . Since the third and fourth components correspond to how much of x 0 lies in eigenspaces with eigenvalue < 1, then these terms exponentially decay as powers of A are applied, hence we determine that in the long run 59 / 90 65 . 56% of patients will recover, while 31 / 90 34 . 44% of patients will die.

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