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

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

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

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

D. 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, we need to determine the total change in position and then divide that by the total time it took for that change.

1. **Determine the total change in position:**
- The dolphin starts at its highest point at +3.5 meters (above surface).
- It dives to -10 meters (below surface).
- The total change in position = final position - initial position = -10 m - 3.5 m = -13.5 m.

2. **Total time taken:**
- The time taken for this change is 12.5 seconds.

3. **Average rate of change:**
- Average rate of change = total change in position / total time
- = -13.5 m / 12.5 s = -1.08 m/s.

Thus, the average rate of change in the dolphin’s position is -1.08 meters/second.

So, the correct answer is:

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