Question

one spring day, josiah noted the time of day and the temperature, in degrees fahrenheit. his findings are as follows: at 6 a.m., the temperature was 52° f. for the next 3 hours, the temperature rose 2° per hour. for the next 5 hours, it rose 3° per hour. the temperature then stayed steady until 6 p.m. for the next 4 hours, the temperature dropped 2° per hour. the temperature then dropped steadily until the temperature was 57° at midnight. on the set of axes below, graph josiahs data. click twice to plot a segment. click a segment to delete it.

Explanation:

Step1: Determine time intervals and temperature changes

• 6 a.m. to 9 a.m. (3 hours): Temperature starts at \(52^\circ\)F, rises \(2^\circ\) per hour. So at 9 a.m., temperature is \(52 + 3\times2 = 58^\circ\)F.
• 9 a.m. to 2 p.m. (5 hours): Rises \(3^\circ\) per hour. At 2 p.m., temperature is \(58 + 5\times3 = 73^\circ\)F.
• 2 p.m. to 6 p.m. (4 hours): Stays steady at \(73^\circ\)F.
• 6 p.m. to 10 p.m. (4 hours): Drops \(2^\circ\) per hour. At 10 p.m., temperature is \(73 - 4\times2 = 65^\circ\)F.
• 10 p.m. to midnight (2 hours): Drops from \(65^\circ\)F to \(57^\circ\)F, so rate is \(\frac{65 - 57}{2}= 4^\circ\) per hour (but we just need the endpoints: 10 p.m. (\(65^\circ\)F) and midnight (\(57^\circ\)F)).

Step2: Plot the points

• 6 a.m.: \((0, 52)\) (let 6 a.m. be \(t = 0\))
• 9 a.m.: \((3, 58)\)
• 2 p.m.: \((8, 73)\) (3 + 5 = 8 hours after 6 a.m.)
• 6 p.m.: \((12, 73)\) (8 + 4 = 12 hours after 6 a.m.)
• 10 p.m.: \((16, 65)\) (12 + 4 = 16 hours after 6 a.m.)
• Midnight: \((18, 57)\) (16 + 2 = 18 hours after 6 a.m.)

Then connect the points with line segments for each interval.

Answer:

To graph the data, plot the points \((0, 52)\), \((3, 58)\), \((8, 73)\), \((12, 73)\), \((16, 65)\), \((18, 57)\) and connect them with line segments for each time interval (rising, steady, falling) as calculated.