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

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 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 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.

Answer 1

To find the average rate of change in the dolphin's position, we can use the formula:

\[ \text{Average Rate of Change} = \frac{\text{Change in Position}}{\text{Change in Time}} \]

1. Calculate the Change in Position:

   • The dolphin jumped to 3.5 meters above the surface (which we can consider as +3.5 meters) and then dove to 10 meters below the surface (which we consider as -10 meters).
   • Therefore, the change in position is:
     \[ \text{Change in Position} = \text{Final Position} - \text{Initial Position} = -10 , \text{meters} - 3.5 , \text{meters} = -13.5 , \text{meters} \]

2. Calculate the Change in Time:

   • The time taken to go from the highest point to the lowest depth is given as 12.5 seconds.

3. Calculate the Average Rate of Change: \[ \text{Average Rate of Change} = \frac{-13.5 , \text{meters}}{12.5 , \text{seconds}} \approx -1.08 , \text{meters/second} \]

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

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