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Cell[CellGroupData[{
Cell["Calculus: The Language of Change", "Title"],
Cell[TextData[{
StyleBox["Exercise Set 2.6\n",
FontVariations->{"Underline"->True}],
"Calculus and the S-I-R Invariant"
}], "Subtitle"],
Cell["by Kevra Tanke ", "Subsubtitle"],
Cell[CellGroupData[{
Cell[TextData[StyleBox[
"Exercise 1 : Math Nerd Fever ", "Subtitle"]], "Subtitle"],
Cell["\<\
At the beginning of the semester last year, 96% of the students were not \
interested in calculus, but word of this chapter spread around campus \
infecting the population with a mythical disease Math Nerd Fever. Victims of \
the disease find that they become interested in calculus - and stay that way, \
though they are only successful in spreading the infection for a brief period \
when they are first excited about the chapter. At the end of the last \
academic year, 44% of the population was interested in calculus. What is the \
contact number for Math Nerd Fever? On the average, how many new math nerds \
does each infected student create?\
\>", "Text"],
Cell[CellGroupData[{
Cell["Solution ", "Subsection"],
Cell[TextData[{
"From the text we know that c (the number of contacts) is approximately:\n\n\
\tc \[TildeTilde] ",
Cell[BoxData[
\(TraditionalForm
\`\((Log\ [s[\[Infinity]]] - Log[s[0]])\)/
\((s[\[Infinity]] - s[0])\)\)]]
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Cell[TextData[
"We are given that 96 percent are initially susceptable so s[0] = .96 and \
that the final value is 56 percent (100-44) so s[\[Infinity]] is .56. "],
"Text"],
Cell[BoxData[
RowBox[{"c", " ", "=", " ",
FormBox[\(\(Log\ [ .56] - Log[ .96]\)\/\( .56 - .96\)\),
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Cell["\<\
So the average total number of contacts per infectious person is about 1.3.\
\>", "Text"]
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Cell[CellGroupData[{
Cell[TextData[StyleBox["Exercise 2 ", "Subtitle"]], "Subtitle"],
Cell["\<\
Suppose we measure a and b in a college population for a new strain of flu. \
What limitations would there be in using these parameters in predicting an \
epidemic in a nursing home?\
\>", "Text"],
Cell[CellGroupData[{
Cell["Solution ", "Subsection"],
Cell["\<\
The daily rate of contacts per infective, a, for a college population would \
most likely be larger than that for a nursing home since the student \
population would probably be larger and more mobile.
The probable difference in age may or may not affect the number of days \
infective, so b may not be the same value for both groups.
Also to be considered: the initial values of s, i and r may be different for \
the two populations.\
\>", "Text"]
}, Open ]]
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Cell[TextData[StyleBox["Exercise 3 ", "Subtitle"]], "Subtitle"],
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