On any given day, a student is either healthy or ill. Of the students who are healthy today, 95 percent will be healthy tomorrow. Of the students who are ill today, 55 percent will be ill tomorrow. Let xo (respectively yo) be the proportion of students who are healthy (respectively ill) on Monday. Let xn (resp. Yn) be the proportion of students who are healthy (resp. ill) after n days. You may define a matrix A: а Example of a 2 × 2 matrix A = such that (: :)(:)-() a b d Xn Xn+1 Yn Yn+1 for all n > 0. Suppose that 20 percent of students are ill on Monday. What percentage of students will still be ill on Tuesday? on Wednesday? in n days? Your teacher thinks about the attandance to class so he wants to know. From the given information above, you determine the ill student percentage is in the long term (as n gets very large). Note : The answer must be an integer and its value must be between 0 and 100.

College Algebra
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ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section: Chapter Questions
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On any given day, a student is either healthy or ill. Of the students who are healthy
today, 95 percent will be healthy tomorrow. Of the students who are ill today, 55
percent will be ill tomorrow. Let xo (respectively yo) be the proportion of students
who are healthy (respectively ill) on Monday. Let æn (resp. Yn) be the proportion of
students who are healthy (resp. ill) after n days.
You may define a matrix A:
(:)
(: :)(E)-)
Example of a 2 × 2 matrix A =
such that
c d
b
Xn+1
а
Yn
Yn+1
for all n 2 0.
Suppose that 20 percent of students are ill on Monday. What percentage of students will still be ill on Tuesday? on Wednesday? in n days?
Your teacher thinks about the attandance to class so he wants to know.
From the given information above, you determine the ill student percentage is
in the long term (as n gets very large).
Note : The answer must be an integer and its value must be between 0 and 100.
Transcribed Image Text:On any given day, a student is either healthy or ill. Of the students who are healthy today, 95 percent will be healthy tomorrow. Of the students who are ill today, 55 percent will be ill tomorrow. Let xo (respectively yo) be the proportion of students who are healthy (respectively ill) on Monday. Let æn (resp. Yn) be the proportion of students who are healthy (resp. ill) after n days. You may define a matrix A: (:) (: :)(E)-) Example of a 2 × 2 matrix A = such that c d b Xn+1 а Yn Yn+1 for all n 2 0. Suppose that 20 percent of students are ill on Monday. What percentage of students will still be ill on Tuesday? on Wednesday? in n days? Your teacher thinks about the attandance to class so he wants to know. From the given information above, you determine the ill student percentage is in the long term (as n gets very large). Note : The answer must be an integer and its value must be between 0 and 100.
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