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An Outbreak of a Previously Unknown Influenza Occurred on the Campus

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An outbreak of a previously unknown influenza occurred on the campus of the University of Northern South Dakota at Roscoe during the first semester. Due to the contagious nature of the disease, the campus was quarantined and the disease was allowed to run its course. The table below shows the total number P of infected students for the first four weeks of the outbreak on this campus of 2,500 students. t (days) 0246810121416182022242628P1001211461762122543043614285035896837878991017 Logistic  Exponential \begin{array} { | l | c | c | c | c | c | c | c | c | c | c | c | c | c | c | c | } \hline t \text { (days) } & 0 & 2 & 4 & 6 & 8 & 10 & 12 & 14 & 16 & 18 & 20 & 22 & 24 & 26 & 28 \\\hline P & 100 & 121 & 146 & 176 & 212 & 254 & 304 & 361 & 428 & 503 & 589 & 683 & 787 & 899 & 1017 \\\hline \text { Logistic } & & & & & & & & & & & & & & & \\\hline \text { Exponential } & & & & & & & & & & & & & & & \\\hline\end{array} (a) Find a logistic model for the data. Complete the table with predicted values using this model.(b) Find an exponential model for these data. Complete the table with predicted values using this model.(c) Compare your findings in parts (a) and (b) above. For what values would you consider both models to be a good fit for the data? Which model provides the best fit for the data? Justify your choice.

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Definitions:

Self-Esteem

The perception and evaluation of one's own worth or value.

Socioemotional Selectivity Theory

A theory suggesting that as people age, they shift their priorities and social interactions towards more emotionally fulfilling relationships and experiences.

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Platforms or structures made up of individuals or organizations interconnected through various social relationships, such as friendship, kinship, common interests, or shared knowledge.

Agoraphobia

Fear of open, crowded places.

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