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Let's work through the problem in your image:

### 4a) Drawing the Elevation vs Time Graph
The table shows the elevation at different levels during Rachel's climb. The levels correspond to points in time, and the elevations are in meters. Plotting these would give us an "elevation vs. time" graph. The points you will plot are:
- (Level 2, 2100 m)
- (Level 3, 2400 m)
- (Level 4, 2700 m)
- (Level 5, 2700 m)
- (Level 6, 3100 m)
- (Level 7, 3400 m)
- (Level 8, 3400 m)
- (Level 9, 3700 m)
- (Level 10, 3740 m)

To draw the graph, you'll put levels on the x-axis and elevation on the y-axis. The graph will start at Level 2 with an elevation of 2100 meters and proceed with the points in the table.

### 4b) Calculating Rachel’s Average Speed
The average speed for each part of the climb can be calculated by finding the difference in elevation between two levels, then dividing by the time interval. 

1. From Level 2 to 3: 
   \[
   \text{Speed} = \frac{2400 - 2100}{1 \text{ level}} = 300 \text{ m/level}
   \]

2. From Level 3 to 4: 
   \[
   \text{Speed} = \frac{2700 - 2400}{1 \text{ level}} = 300 \text{ m/level}
   \]

3. From Level 4 to 5: 
   \[
   \text{Speed} = \frac{2700 - 2700}{1 \text{ level}} = 0 \text{ m/level}
   \]

4. From Level 5 to 6: 
   \[
   \text{Speed} = \frac{3100 - 2700}{1 \text{ level}} = 400 \text{ m/level}
   \]

5. From Level 6 to 7: 
   \[
   \text{Speed} = \frac{3400 - 3100}{1 \text{ level}} = 300 \text{ m/level}
   \]

6. From Level 7 to 8: 
   \[
   \text{Speed} = \frac{3400 - 3400}{1 \text{ level}} = 0 \text{ m/level}
   \]

7. From Level 8 to 9: 
   \[
   \text{Speed} = \frac{3700 - 3400}{1 \text{ level}} = 300 \text{ m/level}
   \]

8. From Level 9 to 10: 
   \[
   \text{Speed} = \frac{3740 - 3700}{1 \text{ level}} = 40 \text{ m/level}
   \]

### 4c) Drawing Speed vs Time Graph
To draw the "speed vs. time" graph, the x-axis will represent the levels (time), and the y-axis will represent the speed. The speeds calculated above for each section will be the y-values plotted.

### 5) Graph of Water Levels for Containers
- **For a 2L plastic pop bottle**: The water level will rise steadily, producing a linear graph because the bottle has uniform cross-sections.
- **For a vase**: If the vase narrows at the bottom and widens at the top, the water level will rise quickly at first, then more slowly as the vase's cross-sectional area increases. The graph will start steep and flatten out over time.

Would you like help with specific graphs or further clarifications on any part of this problem?

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Here are 5 related questions you might want to explore:
1. How do we calculate average speed if the time intervals are not constant?
2. What would happen to the speed vs time graph if Rachel stopped for a break during the climb?
3. How would we calculate Rachel's total average speed for the entire climb?
4. What changes in the graph if Rachel descended instead of climbed?
5. How does the shape of the container affect the water level graph?

**Tip**: When plotting graphs, make sure to label the axes and provide units to make the data clear and understandable.

Using the information given and the table, draw an elevation vs. time graph to describe Rachel’s climb, calculate her average speed over each part of her climb, and draw a speed vs. time graph to describe her climb.

Learn how to draw an elevation vs. time graph for Rachel’s climb, calculate her average speed, and create a speed vs. time graph based on elevation data. This math problem involves key concepts like linear motion, speed calculation, and graphing. Suitable for Grades 9-10.

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