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In this exercise, you're asked to estimate the average rate of change of the percentage of new employees in professional services from 2008 to 2012, 2012 to 2017, and from 2008 to 2017, using the provided graph.

Let's break this down:

### Overview of the Graph
- **X-axis (horizontal)**: Represents the years from 2008 to 2017.
- **Y-axis (vertical)**: Shows the percentage change in employment.

### Steps:
1. **From 2008 to 2012**:
   - In 2008, the percentage change starts around **-6%** (negative growth).
   - By 2012, it has increased to about **+2%**.
   - The **average rate of change** is the slope:  
     \[
     \text{Rate of Change} = \frac{\text{Change in percentage}}{\text{Change in time}} = \frac{2 - (-6)}{2012 - 2008} = \frac{8}{4} = 2 \% \text{ per year}
     \]

2. **From 2012 to 2017**:
   - In 2012, the percentage change is around **2%**.
   - In 2017, it remains around **2%**.
   - Therefore, the **average rate of change** here is:
     \[
     \text{Rate of Change} = \frac{2 - 2}{2017 - 2012} = \frac{0}{5} = 0 \% \text{ per year}
     \]

3. **From 2008 to 2017**:
   - From 2008, starting at **-6%**, to 2017, reaching **2%**.
   - The **average rate of change**:
     \[
     \text{Rate of Change} = \frac{2 - (-6)}{2017 - 2008} = \frac{8}{9} \approx 0.89 \% \text{ per year}
     \]

### Summary:
- **2008 to 2012**: Average rate of change ≈ **2% per year**.
- **2012 to 2017**: Average rate of change = **0% per year**.
- **2008 to 2017**: Average rate of change ≈ **0.89% per year**.

Would you like more detailed steps for any part of the solution? 

Here are five related questions to further your understanding:
1. What does a negative percentage change in employment indicate about a specific industry?
2. How would the average rate of change differ if there were significant fluctuations between years?
3. How can this data be used to predict future employment trends in professional services?
4. Can the average rate of change alone provide a complete picture of employment trends in an industry?
5. How would you calculate the average rate of change for smaller intervals within the 2008-2012 period?

**Tip**: When interpreting graphs, be mindful of whether the y-axis shows percentages or absolute values to avoid confusion in rate calculations.

Estimate the average rate of change of the percentage of new employees in professional services from 2008 to 2012, from 2012 to 2017, and from 2008 to 2017, using the provided graph.

Learn how to estimate the average rate of change in professional services employment between 2008 and 2017 using a graph. This problem covers key concepts in rate of change and graphical interpretation. Suitable for students in Grades 9-12.

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