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Here is the graph modeling the height of a person on the Ferris wheel over time. The important features are:

- **Amplitude (14 feet)**: The radius of the Ferris wheel, which defines the distance from the center to the highest or lowest point.
- **Period (32 seconds)**: The time for one full revolution.
- **Vertical shift (16 feet)**: The center of the wheel is 16 feet above the ground.
- **Maximum height (30 feet)**: The person reaches this height after 7 seconds.
- **Minimum height (2 feet)**: The lowest point reached by the person.

Let me know if you want further details or have any questions.

Here are some related questions:
1. What would happen to the graph if the Ferris wheel's diameter increased?
2. How would the graph change if the period was longer?
3. What is the height after 10 seconds?
4. How would the equation change if the person starts at the top?
5. What would be the phase shift if the person reaches the top after 5 seconds?

**Tip**: In trigonometric modeling, phase shifts help position sinusoidal functions based on specific initial conditions.

A Ferris wheel at a carnival makes 1 revolution every 32 seconds and its diameter is 28 feet. A person gets on the Ferris wheel, and after 7 seconds, reaches the top, 30 feet above the ground.

This problem involves modeling the height of a person on a Ferris wheel using trigonometric functions. The Ferris wheel makes one revolution every 32 seconds and has a diameter of 28 feet. The person reaches the top, 30 feet above the ground, after 7 seconds. Learn how to apply amplitude, period, and vertical shift in this real-world problem. Suitable for students in Grades 10-12.

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