33. Temperature On September 10 in midstate New Hampshire, the temperature at 6 A.M. was \( 45^{\circ} \mathrm{F} \). At 2 P.M. on the same day, the temperature was \( 77^{\circ} \mathrm{F} \). Find the average rate of change in temperature per hour.

To find the average rate of change in temperature per hour, we can use the formula for the average rate of change: \[ \text{Average Rate of Change} = \frac{\text{Change in Temperature}}{\text{Change in Time}} \] 1. **Determine the change in temperature:** - Temperature at 6 A.M. = \( 45^{\circ} \mathrm{F} \) - Temperature at 2 P.M. = \( 77^{\circ} \mathrm{F} \) Change in temperature: \[ \Delta T = 77^{\circ} \mathrm{F} - 45^{\circ} \mathrm{F} = 32^{\circ} \mathrm{F} \] 2. **Determine the change in time:** - From 6 A.M. to 2 P.M. is 8 hours. Change in time: \[ \Delta t = 8 \text{ hours} \] 3. **Calculate the average rate of change:** \[ \text{Average Rate of Change} = \frac{32^{\circ} \mathrm{F}}{8 \text{ hours}} = 4^{\circ} \mathrm{F} \text{ per hour} \] Thus, the average rate of change in temperature per hour is \( 4^{\circ} \mathrm{F} \) per hour.