To determine which equation represents the temperature [tex]\( t \)[/tex] at hour [tex]\( h \)[/tex] in Burrtown, let's consider the given information.
1. Initial Condition:
The temperature starts at [tex]\( 25^{\circ} F \)[/tex] at midnight. This implies that when [tex]\( h = 0 \)[/tex], [tex]\( t = 25 \)[/tex].
2. Rate of Change:
The temperature drops by 3 degrees every hour. This means that for every hour that passes, the temperature decreases by 3 degrees.
To form the equation, we'll start with the initial temperature and consider the effect of the hourly decrease:
- Initial Value:
At [tex]\( h = 0 \)[/tex], [tex]\( t = 25 \)[/tex].
- Hourly Decrease:
For each hour [tex]\( h \)[/tex], the temperature decreases by [tex]\( 3 \cdot h \)[/tex].
Combining these two observations, the temperature [tex]\( t \)[/tex] at any hour [tex]\( h \)[/tex] can be modeled as:
[tex]\[ t = 25 - 3h \][/tex]
Where:
- [tex]\( 25 \)[/tex] is the starting temperature at [tex]\( h = 0 \)[/tex].
- [tex]\( -3h \)[/tex] accounts for the drop in temperature by 3 degrees each hour.
Now, let's compare our derived equation to the provided options:
- A. [tex]\( t = 3h + 25 \)[/tex] (This option suggests the temperature increases by 3 degrees each hour, which is incorrect.)
- B. [tex]\( t = -25h + 3 \)[/tex] (This option does not reflect the initial temperature correctly and has an incorrect slope.)
- C. [tex]\( t = 25h - 3 \)[/tex] (This option suggests a linear increase in temperature, then a fixed drop, which does not match the scenario.)
- D. [tex]\( t = -3h + 25 \)[/tex] (This option correctly represents the temperature starting at [tex]\( 25 \)[/tex] and decreasing by 3 degrees each hour.)
Therefore, the correct equation that represents the temperature [tex]\( t \)[/tex] at hour [tex]\( h \)[/tex] is:
[tex]\[ \boxed{t = -3h + 25} \][/tex]
