College

The function [tex]f(t) = 349.2(0.98)^t[/tex] models the relationship between [tex]t[/tex], the time an oven spends cooling, and the temperature of the oven.

**Oven Cooling Time**

[tex]
\[
\begin{array}{|c|c|}
\hline
\text{Time (minutes)} & \text{Oven temperature (degrees Fahrenheit) } f(t) \\
\hline
5 & 315 \\
\hline
10 & 285 \\
\hline
15 & 260 \\
\hline
20 & 235 \\
\hline
25 & 210 \\
\hline
\end{array}
\]
[/tex]

For which temperature will the model most accurately predict the time spent cooling?

A. 0
B. 100
C. 300
D. 400

Answer :

We start by noting that the oven's cooling data ranges from approximately [tex]$315^\circ\text{F}$[/tex] (after 5 minutes) to about [tex]$210^\circ\text{F}$[/tex] (after 25 minutes). The model

[tex]$$ f(t)=349.2\,(0.98)^t $$[/tex]

was determined based on these data. This means that the model’s predictions are most reliable for temperatures within the measured range, which is between about [tex]$210^\circ\text{F}$[/tex] and [tex]$315^\circ\text{F}$[/tex].

Given the temperature options:

[tex]$$ 0^\circ\text{F},\quad 100^\circ\text{F},\quad 300^\circ\text{F},\quad 400^\circ\text{F} $$[/tex]

we can see that only [tex]$300^\circ\text{F}$[/tex] falls within the range of the recorded data.

Thus, the model will most accurately predict the cooling time when the oven temperature is about [tex]$300^\circ\text{F}$[/tex].