A linear model fits a temperature that changes by the same amount over equal time intervals. Use the temperature at hour zero as the starting value, then put degrees per hour in front of the hour variable. If the change is given over several hours, divide by that number of hours first; treating the whole change as a per-hour rate makes the model too steep.
Hints
- Hint 1
The starting value is the temperature when the input is zero. Since counts hours after 6 a.m., what time does represent, and what temperature belongs there?
- Hint 2
Slope means the temperature change for one hour here. Divide the given change in degrees by the number of hours it takes before putting a number in front of .
Step-by-step
Start with the temperature and find the hourly rate
Step 1Find the starting temperature
No Desmos needed. The story gives the start and a constant rate directly. At 6 a.m., , so . In a linear model , is the starting temperature. So .
- Step 2
Convert the rise to degrees per hour
The temperature rises degrees in hours. Divide the rise by the time to get the slope, the rise in one hour:
A slope uses degrees per hour, not hours per degree. The -degree rise takes two hours; it doesn't happen every hour.
- Step 3
Write the temperature model
Add the hourly rise times to the starting temperature:
The plus sign matches the rising temperature. This models the temperature for hours after 6 a.m. Choice C.