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 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 −0.52 meters/second.
The quotient that describes the rate of change in the dolphin’s position is negative 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 1.08 meters/second.

GPT-4o mini · Answer

To find the average rate of change in the dolphin's position, we first determine the total change in position from its highest point to its lowest point.

The dolphin reaches an altitude of 3.5 meters above the water and then dives to 10 meters below the surface.

To find the total change in position, we need to consider the dolphin's position relative to the water surface. We will represent the position above the water as positive and the position below the water as negative.

The highest point above the water: +3.5 meters
The lowest point below the water: -10 meters

Now, we calculate the total change in position:

Total change in position = Final position - Initial position
= (-10) - (3.5)
= -10 - 3.5
= -13.5 meters

The time taken for this change is 12.5 seconds.

Now we can find the average rate of change (which is a quotient of change in position and time):

Average rate of change = Total change in position / Total time
= -13.5 meters / 12.5 seconds
= -1.08 meters/second

So, the quotient that describes the rate of change in the dolphin's position is −1.08 meters/second.

Thus, the correct response is:

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