Answer :
The function is based on experimental data collected for temperatures between [tex]$210^\circ\text{F}$[/tex] and [tex]$315^\circ\text{F}$[/tex]. Here is a detailed explanation:
1. The given table shows that when the oven cools, the observed temperatures range from [tex]$315^\circ\text{F}$[/tex] (at [tex]$t = 5$[/tex]) down to [tex]$210^\circ\text{F}$[/tex] (at [tex]$t = 25$[/tex]).
2. When using a model, predictions are most reliable within the range of the observed data. That is, predictions for temperatures within the interval
[tex]$$
[210^\circ\text{F},\, 315^\circ\text{F}]
$$[/tex]
are expected to be more accurate.
3. Among the candidate temperatures provided ([tex]$0^\circ\text{F}$[/tex], [tex]$100^\circ\text{F}$[/tex], [tex]$300^\circ\text{F}$[/tex], and [tex]$400^\circ\text{F}$[/tex]), only [tex]$300^\circ\text{F}$[/tex] lies within the measured interval from [tex]$210^\circ\text{F}$[/tex] to [tex]$315^\circ\text{F}$[/tex].
4. Therefore, the model will most accurately predict the time spent cooling when the oven has a temperature of
[tex]$$
300^\circ\text{F}.
$$[/tex]
Thus, the answer is [tex]$\boxed{300}$[/tex].
1. The given table shows that when the oven cools, the observed temperatures range from [tex]$315^\circ\text{F}$[/tex] (at [tex]$t = 5$[/tex]) down to [tex]$210^\circ\text{F}$[/tex] (at [tex]$t = 25$[/tex]).
2. When using a model, predictions are most reliable within the range of the observed data. That is, predictions for temperatures within the interval
[tex]$$
[210^\circ\text{F},\, 315^\circ\text{F}]
$$[/tex]
are expected to be more accurate.
3. Among the candidate temperatures provided ([tex]$0^\circ\text{F}$[/tex], [tex]$100^\circ\text{F}$[/tex], [tex]$300^\circ\text{F}$[/tex], and [tex]$400^\circ\text{F}$[/tex]), only [tex]$300^\circ\text{F}$[/tex] lies within the measured interval from [tex]$210^\circ\text{F}$[/tex] to [tex]$315^\circ\text{F}$[/tex].
4. Therefore, the model will most accurately predict the time spent cooling when the oven has a temperature of
[tex]$$
300^\circ\text{F}.
$$[/tex]
Thus, the answer is [tex]$\boxed{300}$[/tex].
