To find the average rate of change in the dolphin's position, we first calculate the total change in the dolphin's position from its highest point above the water to its lowest point below the water.
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Determine the highest point: The dolphin reaches an altitude of 3.5 meters above the surface of the water.
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Determine the lowest point: The dolphin dives to 10 meters below the surface of the water. Since below the surface is considered a negative position, we can represent this as -10 meters.
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Calculate the total change in position: \[ \text{Change in position} = \text{Lowest point} - \text{Highest point} = -10 , \text{meters} - 3.5 , \text{meters} = -10 - 3.5 = -13.5 , \text{meters} \]
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Determine the time taken: The dolphin moved from its highest point to its lowest point in 12.5 seconds.
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Calculate the average rate of change: The average rate of change of the dolphin's position can be calculated using the formula: \[ \text{Average rate of change} = \frac{\text{Change in position}}{\text{Time}} = \frac{-13.5 , \text{meters}}{12.5 , \text{seconds}} \] \[ \text{Average rate of change} = -1.08 , \text{meters per second} \]
The quotient represents the average rate of change of the dolphin's position, which is -1.08 meters per second. The negative sign indicates that the dolphin is moving downward, on average, over the time period considered.
Final answer: -1.08 m/s (to the nearest hundredth).