To find the average rate of change in the dolphin's position, we need to determine the total change in position and the time over which this change occurs.
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Calculate the highest point: The dolphin reaches a height of 3.5 meters above the surface of the water.
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Calculate the lowest point: The dolphin dives to a depth of 10 meters below the surface of the water. In terms of position relative to the surface, this would be -10 meters (below the water).
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Total change in position:
- Starting position (highest point): 3.5 meters
- Ending position (lowest point): -10 meters
- Total change in position = Ending position - Starting position \[ \text{Total change} = -10 - 3.5 = -13.5 \text{ meters} \]
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Time taken: The dolphin takes 12.5 seconds for this change.
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Average rate of change: \[ \text{Average rate of change} = \frac{\text{Total change in position}}{\text{Time}} = \frac{-13.5 \text{ meters}}{12.5 \text{ seconds}} = -1.08 \text{ meters/second} \]
Thus, the quotient that describes the rate of change in the dolphin’s position is \(-1.08\) meters/second.
The correct response is:
The quotient that describes the rate of change in the dolphin’s position is −1.08 meters/second.