1. **State the problem:** We are given temperature changes over time starting at 6 a.m. with 50°F, and we need to understand the temperature at various times and graph the data. 2. **Identify the time intervals and temperature changes:** - From 6 a.m. to 8 a.m. (2 hours), temperature rises 4° per hour. - From 8 a.m. to 11 a.m. (3 hours), temperature rises 2° per hour. - From 11 a.m. to 6 p.m. (7 hours), temperature stays steady. - From 6 p.m. to 8 p.m. (2 hours), temperature drops 1° per hour. - From 8 p.m. to midnight (4 hours), temperature drops steadily to 59°. 3. **Calculate temperature at key times:** - At 6 a.m.: $T=50$ - At 8 a.m.: $T=50 + 2 \times 4 = 50 + 8 = 58$ - At 11 a.m.: $T=58 + 3 \times 2 = 58 + 6 = 64$ - From 11 a.m. to 6 p.m., temperature steady at $64$ - At 6 p.m.: $T=64$ - At 8 p.m.: $T=64 - 2 \times 1 = 64 - 2 = 62$ - From 8 p.m. to midnight, temperature drops from 62 to 59 over 4 hours. 4. **Find rate of temperature drop from 8 p.m. to midnight:** - Temperature change: $62 - 59 = 3$ degrees over 4 hours. - Rate: $\frac{3}{4} = 0.75$ degrees per hour drop. 5. **Summary of temperature at key times:** - 6 a.m.: 50°F - 8 a.m.: 58°F - 11 a.m.: 64°F - 6 p.m.: 64°F - 8 p.m.: 62°F - 12 midnight: 59°F 6. **Graph description:** - Segment 1 (6 a.m. to 8 a.m.): rising slope with rate 4°/hr - Segment 2 (8 a.m. to 11 a.m.): rising slope with rate 2°/hr - Segment 3 (11 a.m. to 6 p.m.): horizontal line at 64°F - Segment 4 (6 p.m. to 8 p.m.): falling slope with rate 1°/hr - Segment 5 (8 p.m. to midnight): falling slope with rate 0.75°/hr This completes the analysis and data points for graphing Jack's temperature data.