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Answer :
To determine if the temperature in the oven is a function of time, we need to consider the definition of a function. In mathematical terms, a function relates each input to exactly one output. Here, the input is time, and the output is temperature.
Let's break down the situation:
1. Time Periods and Temperatures:
- At 5:00 p.m., the oven is turned on, and the temperature starts at [tex]\(72^\circ F\)[/tex].
- The temperature rises to [tex]\(400^\circ F\)[/tex] over a 10-minute period.
- The oven stays at [tex]\(400^\circ F\)[/tex] for 45 minutes.
- After that, the oven cools down back to [tex]\(72^\circ F\)[/tex] over 60 minutes, reaching this temperature at 6:55 p.m.
2. Analyzing the Temperature Changes:
- During the entire time from turning on the oven until it returns to [tex]\(72^\circ F\)[/tex], at any specific moment, there is only one temperature value of the oven.
3. Function Assessment:
- The temperature at any specific moment of time is unique (i.e., there aren't two different temperatures at the same time).
- This matches the requirement for a function, where each input time corresponds to only one output temperature.
Therefore, we can conclude that:
- It is a function because at any given time, the oven was exactly one temperature.
This explanation aligns with the correct understanding of a function and confirms that the temperature of an oven over time in this scenario is a function.
Let's break down the situation:
1. Time Periods and Temperatures:
- At 5:00 p.m., the oven is turned on, and the temperature starts at [tex]\(72^\circ F\)[/tex].
- The temperature rises to [tex]\(400^\circ F\)[/tex] over a 10-minute period.
- The oven stays at [tex]\(400^\circ F\)[/tex] for 45 minutes.
- After that, the oven cools down back to [tex]\(72^\circ F\)[/tex] over 60 minutes, reaching this temperature at 6:55 p.m.
2. Analyzing the Temperature Changes:
- During the entire time from turning on the oven until it returns to [tex]\(72^\circ F\)[/tex], at any specific moment, there is only one temperature value of the oven.
3. Function Assessment:
- The temperature at any specific moment of time is unique (i.e., there aren't two different temperatures at the same time).
- This matches the requirement for a function, where each input time corresponds to only one output temperature.
Therefore, we can conclude that:
- It is a function because at any given time, the oven was exactly one temperature.
This explanation aligns with the correct understanding of a function and confirms that the temperature of an oven over time in this scenario is a function.
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