Answer :
We are given the model
[tex]$$
f(t) = 349.2 \cdot (0.98)^t,
$$[/tex]
which was obtained using experimental data that shows the oven temperature at several times:
[tex]\[
\begin{array}{|c|c|}
\hline
t \, (\text{minutes}) & f(t) \, (\text{degrees Fahrenheit}) \\
\hline
5 & 315 \\
10 & 285 \\
15 & 260 \\
20 & 235 \\
25 & 210 \\
\hline
\end{array}
\][/tex]
This data indicates that the observed temperatures in the experiment ranged from approximately [tex]$210^\circ F$[/tex] to [tex]$315^\circ F$[/tex]. When using a model, predictions are most reliable when they fall within the range of the data that was used to develop the model.
The multiple choice options for the temperature are [tex]$0^\circ F$[/tex], [tex]$100^\circ F$[/tex], [tex]$300^\circ F$[/tex], and [tex]$400^\circ F$[/tex]. Only the temperature [tex]$300^\circ F$[/tex] lies within the range of the observed temperatures ([tex]$210^\circ F$[/tex] to [tex]$315^\circ F$[/tex]).
Thus, the model will most accurately predict the time spent cooling for a temperature of
[tex]$$\boxed{300^\circ F}.$$[/tex]
[tex]$$
f(t) = 349.2 \cdot (0.98)^t,
$$[/tex]
which was obtained using experimental data that shows the oven temperature at several times:
[tex]\[
\begin{array}{|c|c|}
\hline
t \, (\text{minutes}) & f(t) \, (\text{degrees Fahrenheit}) \\
\hline
5 & 315 \\
10 & 285 \\
15 & 260 \\
20 & 235 \\
25 & 210 \\
\hline
\end{array}
\][/tex]
This data indicates that the observed temperatures in the experiment ranged from approximately [tex]$210^\circ F$[/tex] to [tex]$315^\circ F$[/tex]. When using a model, predictions are most reliable when they fall within the range of the data that was used to develop the model.
The multiple choice options for the temperature are [tex]$0^\circ F$[/tex], [tex]$100^\circ F$[/tex], [tex]$300^\circ F$[/tex], and [tex]$400^\circ F$[/tex]. Only the temperature [tex]$300^\circ F$[/tex] lies within the range of the observed temperatures ([tex]$210^\circ F$[/tex] to [tex]$315^\circ F$[/tex]).
Thus, the model will most accurately predict the time spent cooling for a temperature of
[tex]$$\boxed{300^\circ F}.$$[/tex]
