A dolphin jumped above the surface of the water. It reached an altitude of 3.5 meters above the surface of the water and then dove 10 meters below the surface of the water. It went from its highest point above the water to its lowest depth in 12.5 seconds. Interpret the quotient to describe the average rate of change in the dolphin’s position. Give your answer to the nearest hundredth.(1 point)

Question

A dolphin jumped above the surface of the water. It reached an altitude of 3.5 meters above the surface of the water and then dove 10 meters below the surface of the water. It went from its highest point above the water to its lowest depth in 12.5 seconds. Interpret the quotient to describe the average rate of change in the dolphin’s position. Give your answer to the nearest hundredth.(1 point)
Responses

The quotient that describes the rate of change in the dolphin’s position is −1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is negative 1.08  meters/second.

The quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.

The quotient that describes the rate of change in the dolphin’s position is 0.52 meters/second.
The quotient that describes the rate of change in the dolphin’s position is 0.52 meters/second.

The quotient that describes the rate of change in the dolphin’s position is −0.52 meters/second.
The quotient that describes the rate of change in the dolphin’s position is negative 0.52  meters/second.
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GPT-4o mini · Answer

To calculate the average rate of change in the dolphin's position, we need to determine its overall change in position and the time it took.

Initial Position: The dolphin's highest point is 3.5 meters above the water. We can represent this as +3.5 meters.
Final Position: The dolphin dives to a position of 10 meters below the surface of the water. We can represent this as -10 meters.

Now, we calculate the total change in position:

\[ \text{Change in Position} = \text{Final Position} - \text{Initial Position} = -10 - (3.5) = -10 - 3.5 = -13.5 \text{ meters} \]

Next, we calculate the average rate of change by dividing the change in position by the time taken:

\[ \text{Average Rate of Change} = \frac{\text{Change in Position}}{\text{Time}} = \frac{-13.5 \text{ meters}}{12.5 \text{ seconds}} = -1.08 \text{ meters/second} \]

Thus, the quotient that describes the average 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.