https://file.aiquickdraw.com/mathbot/file/1727021340269dl2iui50.jpg

Let's analyze the given table and answer each of the parts in the question step-by-step:

### Table Information
- **January:** 3.00 (thousand m³)
- **February:** 3.75 (thousand m³)
- **March:** 3.75 (thousand m³)
- **April:** 4.00 (thousand m³)
- **May:** 5.10 (thousand m³)
- **June:** 5.50 (thousand m³)

---

### a) **Plot the data in the table on a graph:**

To plot the dataLet's analyze the given table and answer each of the parts in the question step-by-step:

### Table Information
- **January:** 3.00 (thousand m³)
- **February:** 3.75 (thousand m³)
- **March:** 3.75 (thousand m³)
- **April:** 4.00 (thousand m³)
- **May:** 5.10 (thousand m³)
- **June:** 5.50 (thousand m³)

---

### a) **Plot the data in the table on a graph:**

To plot the 
- Use the **months** on the x-axis.
- Use the **water volume (in thousand m³)** on the y-axis.
- The points to plot would be:
  - (January, 3.00)
  - (February, 3.75)
  - (March, 3.75)
  - (April, 4.00)
  - (May, 5.10)
  - (June, 5.50)

I can help create the graph if you'd like!

---

### b) **Find the rate of change in the volume of water used between consecutive months:**

The rate of change between two consecutive months is calculated by the formula:
\[
\text{Rate of change} = \frac{\text{Change in volume}}{\text{Change in time}}
\]
Here, the time change is always 1 month, so the formula simplifies to the difference in volumes.

| From (Month) | To (Month) | Volume Change (1000 m³) | Rate of Change (1000 m³/month) |
|--------------|------------|--------------------------|---------------------------------|
| January      | February   | \( 3.75 - 3.00 = 0.75 \) | 0.75                           |
| February     | March      | \( 3.75 - 3.75 = 0.00 \) | 0.00                           |
| March        | April      | \( 4.00 - 3.75 = 0.25 \) | 0.25                           |
| April        | May        | \( 5.10 - 4.00 = 1.10 \) | 1.10                           |
| May          | June       | \( 5.50 - 5.10 = 0.40 \) | 0.40                           |

---

### c) **Between which two months is the change in the volume of water used the greatest?**

From the table above, the greatest change occurs between **April and May**, where the rate of change is **1.10 thousand m³/month**.

---

### d) **Determine the average rate of change in the volume of water used between March and June.**

The average rate of change over a longer period (March to June) is given by:
\[
\text{Average Rate of Change} = \frac{\text{Total Change in Volume}}{\text{Total Change in Time (months)}}
\]

- The volume in **March** is 3.75 (thousand m³) and in **June** it is 5.50 (thousand m³).
- The total time between March and June is 3 months.

\[
\text{Average Rate of Change} = \frac{5.50 - 3.75}{3} = \frac{1.75}{3} \approx 0.583 \text{ thousand m³/month}
\]

---

Would you like me to plot the graph for you or provide further details on any part?

Here are 5 related questions:
1. What would the rate of change be between January and March?
2. How would the rate of change be affected if the volume in February was higher than in March?
3. Can you calculate the cumulative volume of water used over the six months?
4. How would the graph change if the water volume decreased in June instead of increasing?
5. What does the average rate of change tell us about water usage between March and June?

**Tip:** When analyzing rate of change in real-world data, consistent units of measurement and time intervals make calculations straightforward!

The following table gives the amount of water that is used on a farm during the first six months of the year:

| Month    | Volume (1000 of m³) |
|----------|---------------------|
| January  | 3.00                |
| February | 3.75                |
| March    | 3.75                |
| April    | 4.00                |
| May      | 5.10                |
| June     | 5.50                |

Answer the following questions:
a) Plot the data in the table on a graph.
b) Find the rate of change in the volume of water used between consecutive months.
c) Between which two months is the change in the volume of water used the greatest?
d) Determine the average rate of change in the volume of water used between March and June.

Analyze water usage on a farm over six months with rate of change calculations between months, average rate of change between March and June, and graphical data representation. Suitable for Grade 8-10 students.

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