To find the average rate of change of the dolphin's position from its highest point to its lowest point, we first need to determine the total change in position and then divide by the time it took for that change.
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Determine the initial and final positions:
- The dolphin jumps to an altitude of 3.5 meters above the surface of the water. This can be considered as +3.5 m.
- The dolphin then dives to a depth of 10 meters below the surface of the water. This can be considered as -10 m.
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Calculate the total change in position:
- The change in position is calculated as follows: \[ \text{Change in position} = \text{Final position} - \text{Initial position} = (-10) - (3.5) = -13.5 \text{ meters} \]
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Determine the time interval:
- The time taken for this change is 12.5 seconds.
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Calculate the average rate of change:
- The average rate of change can be calculated using the formula: \[ \text{Average rate of change} = \frac{\text{Change in position}}{\text{Time}} = \frac{-13.5 \text{ m}}{12.5 \text{ s}} \approx -1.08 \text{ m/s} \]
Now, interpreting the answer options given:
- A) The average rate of change of the dolphin’s position is 1.08. (This is incorrect because it should be negative.)
- B) The quotient that describes the rate of change in the dolphin's position is negative 1.08. (This is correct.)
- C) The quotient that best describes the rate of change in the dolphin's position is 0.52. (This is incorrect.)
- D) The quotient that best describes the rate of change in the dolphin's position is negative 0.52. (This is incorrect.)
The correct interpretation from the provided options is B) the quotient that describes the rate of change in the dolphin's position is negative 1.08.