Question 2

Question

A)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 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

Answer 1

To find the average rate of change in the dolphin's position, we need to calculate the total change in position and divide it by the total time.

1. The dolphin's highest point above the water is +3.5 meters, and its lowest point is -10 meters.

2. To find the total change in position: \[ \text{Total Change} = \text{Final Position} - \text{Initial Position} = (-10) - (3.5) = -10 - 3.5 = -13.5 \text{ meters} \]

3. The time taken for this change is 12.5 seconds.

4. Now, we calculate the average rate of change: \[ \text{Average Rate of Change} = \frac{\text{Total Change}}{\text{Total Time}} = \frac{-13.5 \text{ meters}}{12.5 \text{ seconds}} \approx -1.08 \text{ meters/second} \]

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