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