High School

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**

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

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

A. 0

B. 100

C. 300

D. 400

Answer :

To solve this problem, we need to determine which of the given temperatures—0, 100, 300, or 400—can be predicted with the highest accuracy by the model [tex]\( f(t) = 349.2 \times (0.98)^t \)[/tex] based on the provided data.

### Step-by-Step Solution:

1. Understand the Model:
[tex]\[
f(t) = 349.2 \times (0.98)^t
\][/tex]
This equation models how the temperature of an oven decreases over time [tex]\( t \)[/tex] in minutes.

2. Examine Given Data:
The provided table gives the actual temperatures at specific times:
- At 5 minutes, the temperature is 315°F.
- At 10 minutes, the temperature is 285°F.
- At 15 minutes, the temperature is 260°F.
- At 20 minutes, the temperature is 235°F.
- At 25 minutes, the temperature is 210°F.

3. Identify the Target Temperatures:
We need to assess how closely the model predicts the following temperatures: 0, 100, 300, 400°F.

4. Calculate Model Temperatures and Find Errors:
For each target temperature, we want to determine how well our model can approximate these using the times from the data table.

5. Determine the Best Fit Temperature:
By comparing how close each target temperature can be predicted by the model given the actual data temperatures, we find that the model most accurately predicts a temperature of 0°F. The error associated with predicting a temperature of 0°F is the smallest among all the given options.

Hence, for the given model and data, the temperature for which the model most accurately predicts the time spent cooling is 0°F.