To interpret the average rate of change in the dolphin's position, we first need to determine the total change in position from the highest point above the water to the lowest point below the water.
- The highest point of the dolphin is 3.5 meters above the surface of the water. We can represent this position as +3.5 meters.
- The lowest point of the dolphin is 10 meters below the surface of the water, which we can represent as -10 meters.
Now, we calculate the total change in position (Δy):
\[ \Delta y = \text{Final position} - \text{Initial position} \] \[ \Delta y = (-10) - (3.5) = -10 - 3.5 = -13.5 \text{ meters} \]
This means the dolphin moved a total of -13.5 meters (which is a downward change) from its highest point to its lowest point.
Next, we determine the time it took for this change in position, which is 12.5 seconds.
Now we can calculate the average rate of change (average velocity) using the formula:
\[ \text{Average Rate of Change} = \frac{\Delta y}{\Delta t} \] where Δy is the total change in position and Δt is the total time.
Substituting the values we have:
\[ \text{Average Rate of Change} = \frac{-13.5 \text{ meters}}{12.5 \text{ seconds}} = -1.08 \text{ meters/second} \]
Interpretation:
The average rate of change in the dolphin's position is -1.08 meters per second. This negative value indicates that, on average, the dolphin is diving downward at a rate of 1.08 meters per second from its highest point above the water to its lowest point below the water.