Question

A dolphin jump above the surface of the water. They reach an altitude of 3.5 m above the surface of the water and then throw 10 m below the surface of the water. It went from its highest point above the water to the lowest depth and 12.5 seconds. Interpret the quotient to describe the average rate of change and the dolphins position. Give your answer to the nearest hundred p

Answer 1

The average rate of change can be interpreted as the average speed or velocity of the dolphin as it jumps and dives in the water.

To calculate the average rate of change, we can use the formula:

Average rate of change = Total change in position / Total time taken

The total change in position is the sum of the distance above the surface and below the surface: 3.5 m + 10 m = 13.5 m.

The total time taken is given as 12.5 seconds.

Average rate of change = 13.5 m / 12.5 s

Using a calculator to divide 13.5 by 12.5, we get approximately 1.08.

Therefore, the average rate of change, or the average speed or velocity of the dolphin, is approximately 1.08 meters per second.

Since the dolphin started above the surface of the water, reached a peak height of 3.5 m, and then dove below the surface to a depth of 10 m, we can interpret the positive average rate of change as the dolphin moving upward and downward in the water.