Exercise 1.1.31

Question

Temperature readings $T$ (in $^{\circ}F$) were recorded every two hours from midnight to 2:00 pm in Atlanta on a day in June. The time $t$ was measured in hours from midnight.
        \begin{table}[]\centering
\begin{tabular}{|l|l|l|l|l|l|l|l|l|}
\hline
$t$ & 0  & 2  & 4  & 6  & 8  & 10 & 12 & 14 \ \hline
$T$ & 74 & 69 & 68 & 66 & 70 & 78 & 82 & 86 \ \hline
\end{tabular}
\end{table}
        \begin{enumerate}[label=(\alph*)]
            \item Use the readings to sketch a rough graph of $T$ as a function of $t$.
            \item Use your graph to estimate the temperature at 9:00 AM.
        \end{enumerate}

Khagan Gulusoy · Accepted Answer

\begin{enumerate}[label=(\alph*)]
    \item Note that the $y$-axis starts at $60^{\circ}$.
\end{enumerate}
    \begin{figure}[H] \centering
    \begin{tikzpicture}[scale=0.90]
        \begin{axis}[axis lines=left,xmin=0,xmax=14,ymin=60,ymax=86,xtick={0,2,...,14},ytick={66,71,...,86},xlabel={$	au,$ time of the day}, ylabel={$t$, temperature}]
            \addplot[mark=*, only marks] coordinates {(0, 74) (2,69) (4,68) (6,66) (8,70) (10,78) (12,82) (14,86)}; 
            \addplot[ultra thick, surf, colormap/viridis, domain=0:14] {-x^7/71680 + (17*x^6)/15360 - (79*x^5)/2560 + (307*x^4)/768 - (2443* x^3)/960 + (931*x^2)/120 - (2221*x)/210 + 74};
        \end{axis}
    \end{tikzpicture}
    \end{figure}
\begin{enumerate}[label=(\alph*)]
    \item[(b)] At $t=9$, the temperature will be approximately $74^{\circ}F.$
\end{enumerate}

Exercise 1.1.31

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Exercise 1.1.31

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