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

Answer 1

To find the average rate of change in the dolphin’s position from its highest point to its lowest depth, we start by determining the total change in position.

1. The highest point above the water is +3.5 meters.
2. The lowest point below the water is -10 meters.

To find the total change in position, we calculate: \[ \text{Total change} = \text{Lowest point} - \text{Highest point} = -10 , \text{meters} - 3.5 , \text{meters} = -10 - 3.5 = -13.5 , \text{meters}. \]

Next, we divide this change in position by the total time taken for the change, which is 12.5 seconds: \[ \text{Average rate of change} = \frac{\text{Total change}}{\text{Total time}} = \frac{-13.5 , \text{meters}}{12.5 , \text{seconds}}. \]

Calculating this gives: \[ \text{Average rate of change} = \frac{-13.5}{12.5} \approx -1.08 , \text{meters/second}. \]

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

Therefore, the correct answer is:

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