2. The temperature, in degrees Fahrenheit, of a warming room is given by the function [tex]F(m)=2m+58[/tex], where [tex]m[/tex] is the number of minutes the room has been warming.

a. Find the value of [tex]F(8)-F(2)[/tex]. Show or explain how you found your answer.

[tex]\[ F(8) = 2(8) + 58 = 74 \][/tex]

[tex]\[ F(2) = 2(2) + 58 = 62 \][/tex]

[tex]\[ F(8) - F(2) = 74 - 62 = 12 \][/tex]

b. Give an interpretation for your answer from (a) in the context of this problem. Use proper units in your explanation.

The value of 12 indicates the change in temperature, in degrees Fahrenheit, of the room after warming for 6 additional minutes (from 2 minutes to 8 minutes).

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.