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.