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)%0D%0AResponses%0D%0A%0D%0AThe quotient that describes the rate of change in the dolphin’s position is −0.52 meters/second.%0D%0AThe quotient that describes the rate of change in the dolphin’s position is negative 0.52 meters/second.%0D%0A%0D%0AThe quotient that describes the rate of change in the dolphin’s position is −1.08 meters/second.%0D%0AThe quotient that describes the rate of change in the dolphin’s position is negative 1.08 meters/second.%0D%0A%0D%0AThe quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.%0D%0AThe quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.%0D%0A%0D%0AThe quotient that describes the rate of change in the dolphin’s position is 0.52 meters/second.

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)%0D%0AResponses%0D%0A%0D%0AThe quotient that describes the rate of change in the dolphin’s position is −0.52 meters/second.%0D%0AThe quotient that describes the rate of change in the dolphin’s position is negative 0.52  meters/second.%0D%0A%0D%0AThe quotient that describes the rate of change in the dolphin’s position is −1.08 meters/second.%0D%0AThe quotient that describes the rate of change in the dolphin’s position is negative 1.08  meters/second.%0D%0A%0D%0AThe quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.%0D%0AThe quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.%0D%0A%0D%0AThe quotient that describes the rate of change in the dolphin’s position is 0.52 meters/second.

GPT-4o mini · Answer

To find the average rate of change in the dolphin's position, we need to calculate the total change in position and then divide that by the total time it took for the change.

Identify the highest and lowest positions:
- The dolphin's highest point above the water: +3.5 meters
- The dolphin's lowest point below the water: -10 meters
Calculate the total change in position:
- The change in position = final position - initial position = (-10) - (3.5) = -10 - 3.5 = -13.5 meters
Total time taken:
- The time taken for this change is 12.5 seconds.
Calculate the average rate of change: \[ \text{Average rate of change} = \frac{\text{Total change in position}}{\text{Total time}} = \frac{-13.5 \text{ meters}}{12.5 \text{ seconds}} = -1.08 \text{ meters/second} \]

Thus, the rate of change in the dolphin's position is \(-1.08\) meters/second.

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