Answer :
Let's explain the meaning of each statement related to the temperature of the pork roast:
1. [tex]$f(0)=67$[/tex]: This means that when the pork roast is first placed into the oven, its initial temperature is 67 degrees Fahrenheit. At time [tex]\( t = 0 \)[/tex] hours, the roast has just been put in, so this is the starting temperature.
2. [tex]$f(2.75)=165$[/tex]: This indicates that after being in the oven for 2 hours and 45 minutes (which is expressed as 2.75 hours), the temperature of the roast has risen to 165 degrees Fahrenheit. This tells us how hot it is at that specific time point as the cooking progresses.
3. [tex]$f(2.75)>f(3)$[/tex]: This suggests that after reaching 165 degrees Fahrenheit at 2 hours and 45 minutes, the temperature starts to decrease. At 3 hours, the temperature of the roast is less than it was at 2 hours and 45 minutes. This could imply that the roast has been removed from the oven or that the oven temperature was reduced, causing the roast to cool down.
In summary:
- The roast starts at 67°F when placed in the oven.
- It reaches 165°F after 2 hours and 45 minutes.
- The temperature decreases after 2 hours and 45 minutes, meaning the the temperature at 3 hours is less than 165°F.
1. [tex]$f(0)=67$[/tex]: This means that when the pork roast is first placed into the oven, its initial temperature is 67 degrees Fahrenheit. At time [tex]\( t = 0 \)[/tex] hours, the roast has just been put in, so this is the starting temperature.
2. [tex]$f(2.75)=165$[/tex]: This indicates that after being in the oven for 2 hours and 45 minutes (which is expressed as 2.75 hours), the temperature of the roast has risen to 165 degrees Fahrenheit. This tells us how hot it is at that specific time point as the cooking progresses.
3. [tex]$f(2.75)>f(3)$[/tex]: This suggests that after reaching 165 degrees Fahrenheit at 2 hours and 45 minutes, the temperature starts to decrease. At 3 hours, the temperature of the roast is less than it was at 2 hours and 45 minutes. This could imply that the roast has been removed from the oven or that the oven temperature was reduced, causing the roast to cool down.
In summary:
- The roast starts at 67°F when placed in the oven.
- It reaches 165°F after 2 hours and 45 minutes.
- The temperature decreases after 2 hours and 45 minutes, meaning the the temperature at 3 hours is less than 165°F.
