https://file.aiquickdraw.com/mathbot/file/1726779965317ewwkkrlf.jpg

Let's break down the problem from the image you uploaded. The table shows the growth of a crowd at a rally over a 3-hour period, with the number of people at different time intervals provided. Let's answer the parts of the question one by one:

### Part (a): Average Rate of Change
The average rate of change in the size of the crowd for each half-hour interval is given by the formula:

\[
\text{Average rate of change} = \frac{\text{Change in number of people}}{\text{Change in time (h)}}
\]

We will compute this for each half-hour interval:

1. **From 0.0 h to 0.5 h:**
\[
\frac{176 - 0}{0.5 - 0} = \frac{176}{0.5} = 352 \, \text{people per hour}
\]

2. **From 0.5 h to 1.0 h:**
\[
\frac{245 - 176}{1.0 - 0.5} = \frac{69}{0.5} = 138 \, \text{people per hour}
\]

3. **From 1.0 h to 1.5 h:**
\[
\frac{388 - 245}{1.5 - 1.0} = \frac{143}{0.5} = 286 \, \text{people per hour}
\]

4. **From 1.5 h to 2.0 h:**
\[
\frac{402 - 388}{2.0 - 1.5} = \frac{14}{0.5} = 28 \, \text{people per hour}
\]

5. **From 2.0 h to 2.5 h:**
\[
\frac{432 - 402}{2.5 - 2.0} = \frac{30}{0.5} = 60 \, \text{people per hour}
\]

6. **From 2.5 h to 3.0 h:**
\[
\frac{415 - 432}{3.0 - 2.5} = \frac{-17}{0.5} = -34 \, \text{people per hour}
\]
   - The negative rate indicates a decrease in the crowd size.

### Part (b): What do these numbers represent?
The numbers represent the average rate of change in the crowd size over each half-hour interval. These rates show how quickly the number of people in the crowd is increasing or decreasing during different time periods.

### Part (c): What do positive and negative rates of change mean in this situation?
- A **positive rate of change**

Determine the average rate of change in the size of the crowd for each half hour of the rally. What do these numbers represent? What do positive and negative rates of change mean in this situation?

Learn how to calculate the average rate of change in the size of a crowd at a rally over a 3-hour period using given data points. This exercise involves determining positive and negative rates of change, suitable for students in Grades 9-10.

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