Question

5.2 time and temperature
the graph shows the temperature between noon and midnight in one day in city a.

1. is it warmer at 3:00 p.m. or 9:00 p.m.?
2. approximately when is the temperature highest?
3. find another time that the temperature is the same as it is at 4:00 p.m.
4. does the temperature change more between 1:00 p.m. and 3:00 p.m. or between 3:00 p.m. and 5:00 p.m.?
5. does this graph show that temperature is a function of time, or time is a function of temperature?
6. when the input for the function is 8, what is the output? what does that tell you about the time and temperature?

Explanation:

Step1: Compare 3pm vs 9pm temps

3pm (3hrs after noon): ~55°F; 9pm (9hrs after noon): ~56°F

Step2: Locate peak temperature

Peak at 5hrs after noon (5:00 p.m.)

Step3: Match 4pm temperature

4pm temp ~58°F; matches 7pm (7hrs after noon)

Step4: Calculate temp changes

1-3pm: $55 - 51 = 4^\circ\text{F}$; 3-5pm: $59 - 55 = 4^\circ\text{F}$ (equal change)

Step5: Apply function definition

Each time has one unique temperature.

Step6: Find output at input=8

Input=8 (8hrs after noon, 8pm): output ~57°F

Answer:

1. It is warmer at 9:00 p.m.
2. The temperature is highest at approximately 5:00 p.m.
3. The temperature is the same as at 4:00 p.m. at approximately 7:00 p.m.
4. The temperature changes the same amount (4°F) between both time periods.
5. The graph shows that temperature is a function of time.
6. The output is approximately 57°F. This means at 8:00 p.m. (8 hours after noon), the temperature in City A is about 57°F.