Answer :
We start with the given cooling model for the oven:
[tex]$$
f(t)=349.2(0.98)^t,
$$[/tex]
where [tex]$t$[/tex] is the time in minutes and [tex]$f(t)$[/tex] is the oven temperature in degrees Fahrenheit.
The observed data for the oven temperatures are:
[tex]\[
\begin{array}{|c|c|}
\hline
t \text{ (minutes)} & f(t) \text{ (degrees Fahrenheit)} \\ \hline
5 & 315 \\ \hline
10 & 285 \\ \hline
15 & 260 \\ \hline
20 & 235 \\ \hline
25 & 210 \\ \hline
\end{array}
\][/tex]
Note that the measured temperatures range from about [tex]$210^\circ F$[/tex] to [tex]$315^\circ F$[/tex].
Since the model is derived based on the cooling behavior observed in the table and is most reliable within that measured range, we look at the multiple-choice options: [tex]$0$[/tex], [tex]$100$[/tex], [tex]$300$[/tex], and [tex]$400$[/tex].
Only the temperature [tex]$300^\circ F$[/tex] falls within the range of the observed data where the model was developed. This suggests that when we use the model to predict the cooling time for a temperature of [tex]$300^\circ F$[/tex], the result will be most accurate because it aligns with the data used to develop the model.
Thus, the model will be most accurate for a temperature of
[tex]$$
\boxed{300^\circ F}.
$$[/tex]
[tex]$$
f(t)=349.2(0.98)^t,
$$[/tex]
where [tex]$t$[/tex] is the time in minutes and [tex]$f(t)$[/tex] is the oven temperature in degrees Fahrenheit.
The observed data for the oven temperatures are:
[tex]\[
\begin{array}{|c|c|}
\hline
t \text{ (minutes)} & f(t) \text{ (degrees Fahrenheit)} \\ \hline
5 & 315 \\ \hline
10 & 285 \\ \hline
15 & 260 \\ \hline
20 & 235 \\ \hline
25 & 210 \\ \hline
\end{array}
\][/tex]
Note that the measured temperatures range from about [tex]$210^\circ F$[/tex] to [tex]$315^\circ F$[/tex].
Since the model is derived based on the cooling behavior observed in the table and is most reliable within that measured range, we look at the multiple-choice options: [tex]$0$[/tex], [tex]$100$[/tex], [tex]$300$[/tex], and [tex]$400$[/tex].
Only the temperature [tex]$300^\circ F$[/tex] falls within the range of the observed data where the model was developed. This suggests that when we use the model to predict the cooling time for a temperature of [tex]$300^\circ F$[/tex], the result will be most accurate because it aligns with the data used to develop the model.
Thus, the model will be most accurate for a temperature of
[tex]$$
\boxed{300^\circ F}.
$$[/tex]
