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Cell[CellGroupData[{
Cell["Calculus: The Language of Change", "Title"],
Cell[TextData[{
StyleBox["Problem 4.1\n",
FontVariations->{"Underline"->True}],
"Linear Cooling"
}], "Subtitle"],
Cell["by Wyatt Hadley", "Subsubtitle"],
Cell["\<\
Let C' stand for the rate of cooling of the canary cage of \
temperature C at time t.\
\>", "Text"],
Cell["\<\
What is the relationship between rate of cooling, C', and the temperature, C? \
In other words, what does \"rate of cooling\" mean? For example, which \
units would you use to measure C'?\
\>", "Text"],
Cell["What feature of the graph of C vs. t represents C'?", "Text"],
Cell["What is the physical meaning of C'?", "Text"],
Cell["\<\
Write an equation that says, \"The rate of cooling is proportional to the \
temperature.\"\
\>", "Text"],
Cell["\<\
The rate of cooling (C') is the first derivative of the temperature function \
(C[t]).\
\>", "Commentary"],
Cell["\<\
\"Rate of cooling\" means the speed at which the temperature decreases (how \
fast it goes down).\
\>", "Commentary"],
Cell["\<\
The units to measure C' would be \"degrees/sec\" (the change in temperature \
divided by the change in time.)\
\>", "Commentary"],
Cell["\<\
The slope of the graph of (C[t]) represents C[t]'.\
\>", "Commentary"],
Cell["\<\
The physical meaning of C' is how fast the temperature is changing at a given \
point of time.\
\>", "Commentary"],
Cell["C'[t] = kC where k is negative for cooling.", "Commentary"]
}, Open ]]
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