Let's analyze the given table, which describes the temperature of a cup of coffee over time:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Time (minutes)} & \text{Temperature (degrees Fahrenheit)} \\
\hline
0 & 200 \\
\hline
10 & 180 \\
\hline
20 & 163 \\
\hline
30 & 146 \\
\hline
40 & 131 \\
\hline
50 & 118 \\
\hline
60 & 107 \\
\hline
\end{array}
\][/tex]
### Step-by-Step Analysis
1. Initial Temperature (Time = 0 minutes)
- At the start, when time is 0 minutes, the temperature of the coffee is 200°F.
2. At 10 minutes
- After 10 minutes, the temperature drops to 180°F.
3. At 20 minutes
- After 20 minutes have passed, the temperature further decreases to 163°F.
4. At 30 minutes
- At the 30-minute mark, the temperature is recorded at 146°F.
5. At 40 minutes
- By 40 minutes, the temperature reaches 131°F.
6. At 50 minutes
- At 50 minutes, the temperature continues to decrease and is 118°F.
7. At 60 minutes
- Finally, after 60 minutes, the temperature of the coffee drops to 107°F.
### Graphical Interpretation
To understand the cooling trend better, you might consider plotting the temperature values against time:
- X-axis (Time in minutes): 0, 10, 20, 30, 40, 50, 60.
- Y-axis (Temperature in degrees Fahrenheit): 200, 180, 163, 146, 131, 118, 107.
By plotting these points on a graph, you will observe a downward slope, indicating that the temperature of the coffee decreases over time. The trend suggests that the rate of cooling slows down as the temperature approaches room temperature.
### Summary
The data indicates a consistent decrease in temperature over each 10-minute interval, which can likely be modeled by an exponential decay function, typical for cooling processes according to Newton's Law of Cooling. The exact nature or direct mathematical model is not specified here, but the observed temperatures provide a clear trend of cooling over the given time intervals.
