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Let's work through both parts of the problem.

### Part A:
We are given a table showing the growth of Tonya's sunflower:

| Time (days) | Height (inches) |
|-------------|-----------------|
| 10          | 4               |
| 20          | 8               |
| 30          | 12              |
| 40          | 16              |

It seems that the sunflower's height is increasing at a constant rate. We can check this by looking at the difference in height over equal intervals of time:

- From day 10 to day 20, the height increases by \( 8 - 4 = 4 \) inches.
- From day 20 to day 30, the height increases by \( 12 - 8 = 4 \) inches.
- From day 30 to day 40, the height increases by \( 16 - 12 = 4 \) inches.

The height increases by 4 inches every 10 days, meaning the growth rate is 0.4 inches per day. 

To predict the height at day 55, we can use the growth rate. Starting from day 40 when the height is 16 inches:

- The number of days from day 40 to day 55 is \( 55 - 40 = 15 \) days.
- In 15 days, the sunflower will grow by \( 0.4 \times 15 = 6 \) inches.

Thus, the height at day 55 is \( 16 + 6 = 22 \) inches.

### Part B:
We are given several function options to model the height \( h(t) \) in inches as a function of time \( t \) in days. Based on the data, we need a linear function with a slope that represents the rate of growth (0.4 inches per day) and a y-intercept (height at day 0) of 0, since the plant starts at 0 inches.

The correct function will have a slope of 0.4. Looking at the given options:

- \( A) h(t) = 4t \) (This implies a growth rate of 4 inches per day, which is too high.)
- \( B) h(t) = \frac{1}{4}t \) (This implies a growth rate of 0.25 inches per day, which is too low.)
- \( C) h(t) = \frac{5}{2}t \) (This implies a growth rate of 2.5 inches per day, which is too high.)
- \( D) h(t) = \frac{2}{5}t \) (This implies a growth rate of 0.4 inches per day, which matches the data.)

Therefore, the correct model is \( D) h(t) = \frac{2}{5}t \).

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Do you have any questions or would you like further clarification?

Here are 5 related questions:
1. How would you modify the function if the sunflower's growth was not constant?
2. Can you calculate the growth rate if the height doubled every day?
3. How can we determine the height of the sunflower after 100 days?
4. If the growth rate slowed down after 40 days, how would this affect the function?
5. What would the function look like if the plant stopped growing after 30 days?

**Tip:** Always check the slope of a linear function to verify if it correctly represents the rate of change in a word problem like this.

If the growth of the sunflower continues at the same rate, what is the expected height, in inches, on day 55? Based on the data in the table, which function is an appropriate model for the height, h, in inches, at time t?

Solve a linear growth problem related to sunflower height over time. Learn how to find the growth rate and determine the height of a sunflower on day 55. Suitable for students in Grades 7-9.

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