Answer :
To find the equation that represents the temperature, \( t \), at hour \( h \), given that the temperature in Burrtown starts at \( 25^\circ F \) at midnight (when \( h = 0 \)) and then drops by 3 degrees every hour, follow these steps:
1. Identify the initial condition:
- At \( h = 0 \) (midnight), the temperature \( t \) is \( 25^\circ F \).
2. Determine the rate of change:
- The temperature drops by 3 degrees each hour. This means for every increase of 1 in \( h \), the temperature \( t \) decreases by 3 degrees.
- This rate of change can be expressed as \(-3\) degrees per hour.
3. Formulate the linear equation:
- A linear equation in the form \( t = mh + b \) describes the relationship between \( t \) and \( h \), where \( m \) is the slope, and \( b \) is the y-intercept (initial temperature).
- In this case, since the temperature drops by 3 degrees every hour, \( m \) is \(-3\).
- The initial temperature at \( h = 0 \) is \( 25^\circ F \), so the y-intercept \( b \) is 25.
- Substituting the values, the equation becomes:
[tex]\[ t = -3h + 25 \][/tex]
4. Verify the choices:
- Option A: \( t = -25h + 3 \)
- Incorrect, as the slope and intercept do not match our derived values.
- Option B: \( t = 3h + 25 \)
- Incorrect, as the slope value should be negative due to the drop in temperature.
- Option C: \( t = -3h + 25 \)
- Correct, as it matches the equation derived from the steps above.
- Option D: \( t = 25h - 3 \)
- Incorrect, as the form and values are incorrect per the problem's conditions.
Thus, the correct equation representing the temperature \( t \) at hour \( h \) is:
[tex]\[ t = -3h + 25 \][/tex]
The answer is:
C. [tex]\( t = -3h + 25 \)[/tex]
1. Identify the initial condition:
- At \( h = 0 \) (midnight), the temperature \( t \) is \( 25^\circ F \).
2. Determine the rate of change:
- The temperature drops by 3 degrees each hour. This means for every increase of 1 in \( h \), the temperature \( t \) decreases by 3 degrees.
- This rate of change can be expressed as \(-3\) degrees per hour.
3. Formulate the linear equation:
- A linear equation in the form \( t = mh + b \) describes the relationship between \( t \) and \( h \), where \( m \) is the slope, and \( b \) is the y-intercept (initial temperature).
- In this case, since the temperature drops by 3 degrees every hour, \( m \) is \(-3\).
- The initial temperature at \( h = 0 \) is \( 25^\circ F \), so the y-intercept \( b \) is 25.
- Substituting the values, the equation becomes:
[tex]\[ t = -3h + 25 \][/tex]
4. Verify the choices:
- Option A: \( t = -25h + 3 \)
- Incorrect, as the slope and intercept do not match our derived values.
- Option B: \( t = 3h + 25 \)
- Incorrect, as the slope value should be negative due to the drop in temperature.
- Option C: \( t = -3h + 25 \)
- Correct, as it matches the equation derived from the steps above.
- Option D: \( t = 25h - 3 \)
- Incorrect, as the form and values are incorrect per the problem's conditions.
Thus, the correct equation representing the temperature \( t \) at hour \( h \) is:
[tex]\[ t = -3h + 25 \][/tex]
The answer is:
C. [tex]\( t = -3h + 25 \)[/tex]
