One spring day, Luis noted the time of day and the temperature, in degrees Fahrenheit. His findings are as follows: At 6 a.m., the temperature was 50° F. For the next 4 hours, the temperature rose 4° per hour. For the next 3 hours, it rose 1° per hour. The temperature then stayed steady until 6 p.m. For the next 3 hours, the temperature dropped 2° per hour. The temperature then dropped steadily until the temperature was 60° at midnight. On the set of axes below, graph Luis's data.


Let's break this down step by step to graph Luis's data and understand the temperature changes over time.

### Timeline Breakdown:
1. **6 a.m.**: The temperature was \( 50^\circ F \).
2. **6 a.m. to 10 a.m. (4 hours)**: The temperature increased by \( 4^\circ F \) per hour.
   - By \( 10 \, \text{a.m.} \), the temperature increase was \( 4 \times 4 = 16^\circ F \).
   - So, the temperature at \( 10 \, \text{a.m.} \) was \( 50^\circ F + 16^\circ F = 66^\circ F \).

3. **10 a.m. to 1 p.m. (3 hours)**: The temperature rose \( 1^\circ F \) per hour.
   - By \( 1 \, \text{p.m.} \), the temperature increased \( 1 \times 3 = 3^\circ F \).
   - So, the temperature at \( 1 \, \text{p.m.} \) was \( 66^\circ F + 3^\circ F = 69^\circ F \).

4. **1 p.m. to 6 p.m. (5 hours)**: The temperature remained steady at \( 69^\circ F \).
   
5. **6 p.m. to 9 p.m. (3 hours)**: The temperature dropped \( 2^\circ F \) per hour.
   - By \( 9 \, \text{p.m.} \), the temperature decreased \( 2 \times 3 = 6^\circ F \).
   - So, the temperature at \( 9 \, \text{p.m.} \) was \( 69^\circ F - 6^\circ F = 63^\circ F \).

6. **9 p.m. to midnight (3 hours)**: The temperature dropped steadily until it reached \( 60^\circ F \).
   - At midnight, the temperature was \( 60^\circ F \).

### Points to Plot:

- At \( 6 \, \text{a.m.} \): \( (6, 50) \)
- At \( 10 \, \text{a.m.} \): \( (10, 66) \)
- At \( 1 \, \text{p.m.} \): \( (13, 69) \)
- From \( 1 \, \text{p.m.} \) to \( 6 \, \text{p.m.} \): The temperature stays at \( 69 \), so we have \( (18, 69) \).
- At \( 9 \, \text{p.m.} \): \( (21, 63) \)
- At midnight: \( (24, 60) \)

### Graphing Instructions:
- Plot time on the x-axis from 6 a.m. (6) to midnight (24).
- Plot temperature on the y-axis.
- Connect the points to form a continuous graph, reflecting the changes in temperature.

Would you like to see the graph plotted or need further clarifications?

### Related Questions:
1. What would the temperature be if the temperature rose by 3° per hour after 1 p.m.?
2. How would the graph look if the temperature decreased by 1° per hour instead of 2° after 6 p.m.?
3. What is the average temperature throughout the day based on Luis’s data?
4. How would the graph change if the temperature stayed steady after 9 p.m.?
5. What would happen to the graph if the temperature started at 55°F instead of 50°F?

### Tip: 
Understanding how to represent real-world data as a graph helps improve your ability to model and interpret trends in various contexts.

One spring day, Luis noted the time of day and the temperature, in degrees Fahrenheit. His findings are as follows: At 6 a.m., the temperature was 50° F. For the next 4 hours, the temperature rose 4° per hour. For the next 3 hours, it rose 1° per hour. The temperature then stayed steady until 6 p.m. For the next 3 hours, the temperature dropped 2° per hour. The temperature then dropped steadily until the temperature was 60° at midnight. On the set of axes below, graph Luis's data.

Learn how to graph Luis's temperature observations throughout the day, starting from 50°F at 6 a.m., with a steady rise and fall in temperature. Understand linear relationships, rates of change, and how to plot time vs temperature on a graph. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation