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 negative 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 −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 determine the average rate of change in the dolphin's position from its highest point to its lowest point, we start by noting the total change in height and the time taken.

1. Find the total change in position:

   • The dolphin jumps to an altitude of 3.5 meters above the water.
   • Then, it dives to 10 meters below the surface of the water.
   • We can consider the water's surface as 0 meters. Therefore, the heights are:
     • Highest point: +3.5 meters
     • Lowest point: -10 meters

   The total change in position is: \[ \text{Change in position} = \text{Final position} - \text{Initial position} = -10 - 3.5 = -13.5 \text{ meters} \]

2. Find the time taken:

   • The time taken for this change is given as 12.5 seconds.

3. Calculate the average rate of change: The average rate of change can be calculated using the formula: \[ \text{Average rate of change} = \frac{\text{Change in position}}{\text{Time}} = \frac{-13.5 \text{ meters}}{12.5 \text{ seconds}} = -1.08 \text{ meters/second} \]

Based on this calculation, the correct interpretation of the quotient that describes the average rate of change in the dolphin's position is: The quotient that describes the rate of change in the dolphin’s position is \(-1.08\) meters/second.