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The image shows a question from an Algebra test related to the behavior of a function. The problem involves a plant's growth function modeled by \( h(x) = \frac{3\sqrt{7x}}{2} + 1 \), where \( x \) represents the number of weeks since the plant was planted, and \( h(x) \) represents the plant's height in inches. The table shows \( x \)-values (weeks) from 0 to 5 and the corresponding heights \( h(x) \).

The question asks what happens to the function as the \( x \)-values increase.

We can analyze the function's behavior:

### Function Analysis:
1. The function \( h(x) = \frac{3\sqrt{7x}}{2} + 1 \) involves a square root, which grows more slowly as \( x \) increases. This implies that the rate of growth slows down over time.
2. **Rate of Change**: As \( x \) increases, the value of \( h(x) \) increases, but the increments between the heights (rate of change) decrease.

Thus, the correct answer is:
- **D. The function is increasing, but the average rate of change is decreasing.**

Would you like further details on this explanation? Here are five follow-up questions:

1. What is the significance of a square root in a growth function?
2. How can we find the rate of change from a table of values?
3. What does it mean when a function’s rate of change decreases?
4. How can we graphically represent the function \( h(x) = \frac{3\sqrt{7x}}{2} + 1 \)?
5. How do we compute the derivative to determine the exact rate of change?

**Tip**: Always observe the growth pattern of functions involving square roots, as they typically show decelerating growth.

Jane planted a marigold sapling in her garden and recorded its growth every week. The plant's height, in inches, is modeled by the function h(x), where x is the number of weeks since Jane planted the sapling. What is true of the function as the x-values increase?

Explore the behavior of the plant's growth function modeled as h(x) = (3√(7x))/2 + 1. Learn how the function increases as time progresses but experiences a decreasing rate of change. This problem highlights key concepts in Algebra, including functions and the rate of change.

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