To find the equation that represents the temperature \( T \) at Alicia's house after \( h \) hours, we need to observe the relationship between the hours passed and the temperature.
From the table:
- At hour 0, the temperature is 63°F.
- At hour 1, the temperature is 66°F.
- At hour 2, the temperature is 69°F.
- At hour 3, the temperature is 72°F.
- At hour 4, the temperature is 75°F.
From the data, we can see that the temperature increases by 3°F for each hour that passes:
- From 63°F to 66°F (increase of 3°F over 1 hour)
- From 66°F to 69°F (increase of 3°F over 1 hour)
- From 69°F to 72°F (increase of 3°F over 1 hour)
- From 72°F to 75°F (increase of 3°F over 1 hour)
This indicates that the temperature increases linearly with time, specifically, it increases by 3 degrees for every hour.
We can express this relationship mathematically as:
\[ T = \text{initial temperature} + (\text{change per hour}) \times h \]
In this case, the initial temperature is 63°F, and the change per hour is 3°F. Thus, the temperature after \( h \) hours can be written as:
\[ T = 3h + 63 \]
So, the equation that best represents the temperature \( T \) at Alicia's house after \( h \) hours is:
T = 3h + 63