To find the average rate of change in the dolphin's position, we need to calculate the change in position (displacement) divided by the change in time.
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The highest point the dolphin reaches is 3.5 meters above the water, and the lowest point is 10 meters below the surface. We need to consider the positions relative to the surface of the water:
- The highest point = +3.5 meters
- The lowest point = -10 meters (since it's below the water surface)
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Now, we can calculate the total change in position: \[ \text{Change in position} = \text{Final position} - \text{Initial position} = -10 - 3.5 = -13.5 \text{ meters} \]
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The time taken for this change in position is 12.5 seconds.
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Now, we calculate the average rate of change: \[ \text{Average rate of change} = \frac{\text{Change in position}}{\text{Change in time}} = \frac{-13.5}{12.5} \approx -1.08 \text{ meters/second} \]
Thus, the quotient that describes the rate of change in the dolphin’s position is −1.08 meters/second.
So, the correct interpretation from the given responses is:
The quotient that describes the rate of change in the dolphin’s position is −1.08 meters/second.