https://file.aiquickdraw.com/mathbot/file/1727428854725scsn9cx3.jpg

The problem asks for the multiplicative rate of change of the exponential function graphed. To determine the multiplicative rate, we should analyze the given points on the graph.

### Step-by-Step Solution
1. **Identify Points on the Graph**:
   - Key points are marked: 
     - \((-2, \frac{2}{9})\)
     - \((-1, \frac{2}{3})\)
     - \((0, 2)\)
     - \((1, 6)\)
     - \((2, 18)\)
     - \((3, 54)\)

2. **Find the Multiplicative Rate**:
   - For an exponential function of the form \( y = ab^x \), the multiplicative rate (base \(b\)) can be found by calculating the ratio between consecutive \( y \)-values.
   - Let's use the consecutive points \((0, 2)\) and \((1, 6)\).
   
     \[
     \text{Rate} = \frac{6}{2} = 3
     \]

3. **Confirm with Other Points**:
   - Check other points for consistency:
     \[
     \frac{18}{6} = 3, \quad \frac{54}{18} = 3
     \]

   This confirms that the multiplicative rate of change is consistently 3 across the points.

### Final Answer
The multiplicative rate of change for the exponential function is **3**.

Let me know if you would like a more detailed explanation, or have any questions! 

### Follow-up Questions:
1. How would you express the exponential function given the multiplicative rate?
2. What is the initial value (\(a\)) of the function when \(x = 0\)?
3. How does the multiplicative rate of change affect the growth of the function?
4. What happens to the graph if the multiplicative rate changes to a value less than 1?
5. Can you determine the function’s equation if we only knew two non-consecutive points?

**Tip**: When analyzing exponential graphs, always confirm the multiplicative rate using multiple consecutive points to ensure accuracy.

What is the multiplicative rate of change for the exponential function graphed to the left?

Learn how to calculate the multiplicative rate of change for the exponential function graph with points such as (0, 2), (1, 6), and (2, 18). This example demonstrates key exponential growth concepts suitable for students in Grades 9-12.

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