Answer :
Sure! Let's work through this step by step:
### Part a: Calculate [tex]\( F(8) - F(2) \)[/tex]
1. Define the function: The temperature function is given by [tex]\( F(m) = 2m + 58 \)[/tex].
2. Calculate [tex]\( F(8) \)[/tex]:
- Plug [tex]\( m = 8 \)[/tex] into the function:
[tex]\[
F(8) = 2(8) + 58 = 16 + 58 = 74
\][/tex]
- The temperature of the room after 8 minutes is 74 degrees Fahrenheit.
3. Calculate [tex]\( F(2) \)[/tex]:
- Plug [tex]\( m = 2 \)[/tex] into the function:
[tex]\[
F(2) = 2(2) + 58 = 4 + 58 = 62
\][/tex]
- The temperature of the room after 2 minutes is 62 degrees Fahrenheit.
4. Find [tex]\( F(8) - F(2) \)[/tex]:
- Subtract the temperature at 2 minutes from the temperature at 8 minutes:
[tex]\[
F(8) - F(2) = 74 - 62 = 12
\][/tex]
### Part b: Interpret the result
The difference [tex]\( F(8) - F(2) = 12 \)[/tex] can be interpreted as the change in temperature of the room from the 2nd minute to the 8th minute. In this context, over the 6-minute interval (from minute 2 to minute 8), the temperature of the room increased by 12 degrees Fahrenheit.
### Part a: Calculate [tex]\( F(8) - F(2) \)[/tex]
1. Define the function: The temperature function is given by [tex]\( F(m) = 2m + 58 \)[/tex].
2. Calculate [tex]\( F(8) \)[/tex]:
- Plug [tex]\( m = 8 \)[/tex] into the function:
[tex]\[
F(8) = 2(8) + 58 = 16 + 58 = 74
\][/tex]
- The temperature of the room after 8 minutes is 74 degrees Fahrenheit.
3. Calculate [tex]\( F(2) \)[/tex]:
- Plug [tex]\( m = 2 \)[/tex] into the function:
[tex]\[
F(2) = 2(2) + 58 = 4 + 58 = 62
\][/tex]
- The temperature of the room after 2 minutes is 62 degrees Fahrenheit.
4. Find [tex]\( F(8) - F(2) \)[/tex]:
- Subtract the temperature at 2 minutes from the temperature at 8 minutes:
[tex]\[
F(8) - F(2) = 74 - 62 = 12
\][/tex]
### Part b: Interpret the result
The difference [tex]\( F(8) - F(2) = 12 \)[/tex] can be interpreted as the change in temperature of the room from the 2nd minute to the 8th minute. In this context, over the 6-minute interval (from minute 2 to minute 8), the temperature of the room increased by 12 degrees Fahrenheit.