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Answer :
Sure! Let's go through each statement and explain what they mean in the context of cooking a pork roast:
1. [tex]$f(0) = 67$[/tex]:
- This statement means that when the pork roast was first placed in the oven (at time [tex]\( t = 0 \)[/tex] hours), its initial temperature was 67°F. This is the starting temperature of the roast before it begins to cook.
2. [tex]$f(2.75) = 165$[/tex]:
- This statement tells us that after 2 hours and 45 minutes (or 2.75 hours), the temperature of the pork roast reached 165°F. This is the temperature at that specific time mark.
3. [tex]$f(2.75) > f(3)$[/tex]:
- This statement indicates that the temperature of the pork roast at 2 hours and 45 minutes (165°F) is greater than its temperature at 3 hours. In other words, the roast starts to cool down after reaching 2.75 hours.
Let's summarize the scenario:
- The pork roast started cooking at an initial temperature of 67°F.
- It reached a peak temperature of 165°F after 2 hours and 45 minutes.
- After reaching this peak, the temperature began to decrease, meaning the roast had a lower temperature at 3 hours than it did at 2 hours and 45 minutes.
Therefore, the important takeaway here is that the roast's temperature increased to 165°F and then started to cool down slightly within the next 15 minutes. This cooling could suggest that either the oven was turned off or the roast was removed from the oven at the 2.75-hour mark.
1. [tex]$f(0) = 67$[/tex]:
- This statement means that when the pork roast was first placed in the oven (at time [tex]\( t = 0 \)[/tex] hours), its initial temperature was 67°F. This is the starting temperature of the roast before it begins to cook.
2. [tex]$f(2.75) = 165$[/tex]:
- This statement tells us that after 2 hours and 45 minutes (or 2.75 hours), the temperature of the pork roast reached 165°F. This is the temperature at that specific time mark.
3. [tex]$f(2.75) > f(3)$[/tex]:
- This statement indicates that the temperature of the pork roast at 2 hours and 45 minutes (165°F) is greater than its temperature at 3 hours. In other words, the roast starts to cool down after reaching 2.75 hours.
Let's summarize the scenario:
- The pork roast started cooking at an initial temperature of 67°F.
- It reached a peak temperature of 165°F after 2 hours and 45 minutes.
- After reaching this peak, the temperature began to decrease, meaning the roast had a lower temperature at 3 hours than it did at 2 hours and 45 minutes.
Therefore, the important takeaway here is that the roast's temperature increased to 165°F and then started to cool down slightly within the next 15 minutes. This cooling could suggest that either the oven was turned off or the roast was removed from the oven at the 2.75-hour mark.
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