dolphin jumped above the surface of the water. It reached an altitude of 3.5 meters above the surface ojavascript:void(0);f 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

Responses

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 −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.

Answer 1

To determine the average rate of change in the dolphin’s position, we first need to find the total change in position from the highest point to the lowest point, and then divide by the total time taken.

1. Highest Point Above Water: 3.5 meters

2. Lowest Point Below Water: -10 meters (since below the surface counts as negative depth)

3. Change in Position: Final position - Initial position = -10 meters - 3.5 meters = -10 - 3.5 = -13.5 meters

4. Total Time: 12.5 seconds

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

Therefore, the correct interpretation of the average rate of change in the dolphin's position is:

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