In this question, the real numbers in your answers should be given with three significant digits of accuracy after the decimal point. The public health authorities of a small town have divided the population into three categories: covid-negative, covid-positive, and hospitalised. After performing regular, extensive tests, they have observed that in each successive week:

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
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Chapter7: Percents
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In this question, the real numbers in your answers should be given with three significant digits of accuracy after the decimal point.

The public health authorities of a small town have divided the population into three categories: covid-negative, covid-positive, and hospitalised. After performing regular, extensive tests, they have observed that in each successive week:

  • Among those who are negative, 95% remain so, 4% become positive, and 1% need to be hospitalised.

  • Among those who are positive, 75% recover and become negative, 20% stay positive, and 5% need to be hospitalised.

  • Among those who are hospitalised, 60% recover and become negative, 30% are released from hospital but remain positive, and 10% remain hospitalised.

(a) After representing the population in a given week as a column vector v=[n;p;h], where n,p, and h represent the number of people in the population who are negative, positive, and hospitalised respectively, write down a matrix M for which[n′,p′,h′]=M[n;p;h], where[n′,p′,h′] represents the column vector of negative, positive, and hospitalised members of the population in the following week.

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