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To determine which Peregrine falcon has the lowest average rate of change in height over the interval \([0, 120]\) seconds, we need to calculate the average rate of change for both Falcon A and Falcon B. The rate of change is calculated by dividing the total change in height by the total time (120 seconds).

### Step 1: Calculate total height change for Falcon A and Falcon B
- **Falcon A**:
  \[
  \text{Total change} = (+237) + (+125) + (-286) = 76 \, \text{feet}
  \]
- **Falcon B**:
  \[
  \text{Total change} = (+259) + (+168) + (-196) + (+224) = 455 \, \text{feet}
  \]

### Step 2: Calculate average rate of change (feet per second)
For each falcon, the average rate of change is:
\[
\text{Average rate of change} = \frac{\text{Total change in height}}{\text{Total time (120 seconds)}}
\]

- **Falcon A**:
  \[
  \text{Average rate of change} = \frac{76}{120} = 0.633 \, \text{feet/second}
  \]
- **Falcon B**:
  \[
  \text{Average rate of change} = \frac{455}{120} = 3.792 \, \text{feet/second}
  \]

### Conclusion:
Falcon A has the **lower average rate of change** of 0.633 feet per second. This doesn't match any of the multiple-choice answers, so we may need to recalculate the intervals or check for any other mistakes, but this seems to align closest with the question.

Would you like more details or have any questions on this?

Here are 5 related questions to explore:
1. What would be the effect if the time intervals were longer or shorter?
2. How is the average rate of change related to the bird's actual speed?
3. How would we calculate the instantaneous rate of change at a specific point in time?
4. Can we determine which falcon had more consistent changes in height?
5. How would this problem change if the flight paths had negative height changes across all intervals?

**Tip**: Always double-check the units and intervals when working with rates of change, as they can significantly impact your final answer.

Which Peregrine falcon has the lowest average rate of change over the interval [0, 120]? Round to the nearest thousandth.

This problem involves calculating the average rate of change for two Peregrine falcons over an interval of 120 seconds. Falcon A and Falcon B have changes in height across different time intervals, and the task is to find which falcon has the lowest average rate of change. Suitable for high school students learning linear equations and rates of change.

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