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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 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.

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

1 answer

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

  1. Determine the change in position:

    • The dolphin's highest point above the water is 3.5 meters.
    • The dolphin's lowest point below the water is -10 meters.

    To find the total change in position, we can express these values on a number line where above the water is positive and below the water is negative:

    \[ \text{Total change in position} = \text{Final position} - \text{Initial position} \] \[ \text{Total change in position} = (-10) - (3.5) = -10 - 3.5 = -13.5 \text{ meters} \]

  2. Dividing by the time: The total time taken for this change is 12.5 seconds.

    \[ \text{Average rate of change} = \frac{\text{Total change in position}}{\text{Total time}} = \frac{-13.5 \text{ meters}}{12.5 \text{ seconds}} \]

    Now we calculate this:

    \[ \text{Average rate of change} = -1.08 \text{ meters/second} \]

So, the quotient that describes the rate of change in the dolphin’s position is approximately -1.08 meters/second.

Given the options, the correct response is: The quotient that describes the rate of change in the dolphin’s position is -1.08 meters/second.