Temperature readings T (in ^∘ F ) were recorded every two hours from midnight to 2: 00 PM in Ph

Temperature readings T (in ^∘ F ) were recorded every two...

Temperature readings $T$ (in ${ }^{\circ} \mathrm{F}$ ) were recorded every two hours from midnight to $2: 00 \mathrm{PM}$ in Phoenix on September 10, 2008. The time $t$ was measured in hours from midnight. $$ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline t & 0 & 2 & 4 & 6 & 8 & 10 & 12 & 14 \\ \hline T & 82 & 75 & 74 & 75 & 84 & 90 & 93 & 94 \\ \hline \end{array} $$ (a) Use the readings to sketch a rough graph of $T$ as a function of $t$. (b) Use your graph to estimate the temperature at 9:00 AM .

Temperature readings $T$ (in ${ }^{\circ} \mathrm{F}$ ) were recorded every two hours from midnight to $2: 00 \mathrm{PM}$ in Phoenix on September 10, 2008. The time $t$ was measured in hours from midnight.
$$
\begin{array}{|c|c|c|c|c|c|c|c|c|}
\hline t & 0 & 2 & 4 & 6 & 8 & 10 & 12 & 14 \\
\hline T & 82 & 75 & 74 & 75 & 84 & 90 & 93 & 94 \\
\hline
\end{array}
$$
(a) Use the readings to sketch a rough graph of $T$ as a function of $t$.
(b) Use your graph to estimate the temperature at 9:00 AM .

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Key Concepts

Interpolation

Interpolation is the method used to estimate the value of a function between two known data points. By analyzing the trend between these points, one can approximate the value at any intermediate point. This tool is essential for estimating values where direct measurements are not available, making it widely applicable in various fields of science and engineering.

Graphing Functions from Discrete Data

This concept involves plotting a set of individual data points on a coordinate plane to visually represent the relationship between two variables. It includes marking each point on the graph according to its coordinates and possibly connecting them to depict trends and changes over time or another domain, providing a visual summary of the behavior of the dataset.