An Outbreak of a Previously Unknown Influenza Occurred on the Campus

question 145

Essay

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. $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | c | c | c | c | c | } \hline t \text { (days) } & 0 & 2 & 4 & 6 & 8 & 10 & 12 & 14 & 16 & 18 & 20 & 22 & 24 & 26 & 28 \\\hline P & 100 & 121 & 146 & 176 & 212 & 254 & 304 & 361 & 428 & 503 & 589 & 683 & 787 & 899 & 1017 \\\hline \text { Logistic } & & & & & & & & & & & & & & & \\\hline \text { Exponential } & & & & & & & & & & & & & & & \\\hline\end{array}$$ (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:

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