. A fitness trainer decided to track the combined weight loss of several new customers. She recorded the combined weight loss each month and kept track for 6 months. Identify the best mathematical model with its corresponding R value and tell whether it is a good model. Month 2 9.

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Identify the best mathematical model and it's r^2 value. Is it a good fit?
**Problem:** A fitness trainer decided to track the combined weight loss of several new customers. She recorded the combined weight loss each month and kept track for 6 months. Identify the best mathematical model with its corresponding \( R^2 \) value and tell whether it is a good model.

**Data Table:**

| Month       | 1   | 2   | 3   | 4   | 5   | 6   |
|-------------|-----|-----|-----|-----|-----|-----|
| Weight Loss | 175 | 120 | 95  | 63  | 44  | 33  |

**Model Evaluation:**

1. **Exponential Model, \( R^2 = 0.996 \):**
   - No, 0.966 is too high an \( R^2 \) value.

2. **Quadratic Model, \( R^2 = 0.994 \):**
   - No, 0.994 is too high an \( R^2 \) value.

3. **Exponential Model, \( R^2 = 0.996 \):**
   - Yes, 0.996 is very close to 1.

4. **Quadratic Model, \( R^2 = 0.994 \):**
   - Yes, 0.994 is very close to 1.
Transcribed Image Text:**Problem:** A fitness trainer decided to track the combined weight loss of several new customers. She recorded the combined weight loss each month and kept track for 6 months. Identify the best mathematical model with its corresponding \( R^2 \) value and tell whether it is a good model. **Data Table:** | Month | 1 | 2 | 3 | 4 | 5 | 6 | |-------------|-----|-----|-----|-----|-----|-----| | Weight Loss | 175 | 120 | 95 | 63 | 44 | 33 | **Model Evaluation:** 1. **Exponential Model, \( R^2 = 0.996 \):** - No, 0.966 is too high an \( R^2 \) value. 2. **Quadratic Model, \( R^2 = 0.994 \):** - No, 0.994 is too high an \( R^2 \) value. 3. **Exponential Model, \( R^2 = 0.996 \):** - Yes, 0.996 is very close to 1. 4. **Quadratic Model, \( R^2 = 0.994 \):** - Yes, 0.994 is very close to 1.
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