To analyze the rate of decline in height above the canyon floor over time based on the provided data, we can calculate the change in height for the given time intervals.
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From 0 to 3 minutes: The height decreases from 360 to 280.
- Change in height = 280 - 360 = -80
- Change in time = 3 - 0 = 3 minutes
- Rate of change = -80 / 3 ≈ -26.67 feet per minute
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From 3 to 10 minutes: The height decreases from 280 to 160.
- Change in height = 160 - 280 = -120
- Change in time = 10 - 3 = 7 minutes
- Rate of change = -120 / 7 ≈ -17.14 feet per minute
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From 10 to 14 minutes: The height decreases from 160 to 80.
- Change in height = 80 - 160 = -80
- Change in time = 14 - 10 = 4 minutes
- Rate of change = -80 / 4 = -20 feet per minute
Now, we summarize the rate of change over the entire period:
- The average rate of change over the entire time, from 0 to 14 minutes, involves calculating the total change in height and total time:
- Total change in height = 80 - 360 = -280
- Total time = 14 - 0 = 14 minutes
- Average rate of change = -280 / 14 = -20 feet per minute
Based on this analysis, we can interpret the rate of change of height above the canyon floor over time.
Interpretation: The height above the canyon floor decreases at an average rate of approximately 20 feet per minute. This indicates a consistent decline in height as time progresses, suggesting a linear relationship between height and time.