A bird is flying at an average altitude of 10 meters above the ground. After 3 seconds, it settles on a branch that is 3 meters above the ground. Interpret the quotient to describe the rate of change
The quotient can be interpreted as the rate of change in altitude per unit of time. In this context, the quotient would be 1 meter per second, which means that the bird is descending at a rate of 1 meter per second.
To describe the rate of change, we can calculate the average velocity by dividing the change in altitude by the time it takes for the bird to settle on the branch.
The change in altitude is calculated as follows:
Final altitude - Initial altitude = 3 meters - 10 meters = -7 meters
The time it takes for the bird to settle on the branch is provided as 3 seconds.
Now we can calculate the average velocity using the formula:
Average velocity = Change in altitude / Time taken
Substituting the values, we get:
Average velocity = -7 meters / 3 seconds ≈ -2.33 meters per second
The quotient -2.33 meters per second describes the rate of change of the bird's altitude. The negative sign indicates that the bird is descending or moving downwards at an average rate of approximately 2.33 meters per second.
To interpret the quotient that describes the rate of change, we first need to determine the change that occurred in the given time period.
The bird started flying at an altitude of 10 meters above the ground and then settled on a branch that is 3 meters above the ground. Therefore, the change in altitude is calculated as:
Change in altitude = Final altitude - Initial altitude
= 3 meters - 10 meters
= -7 meters
Now, we need to consider the time it took for this change to occur. In this case, the given time period is 3 seconds.
Thus, the rate of change can be calculated by dividing the change in altitude by the time taken:
Rate of change = Change in altitude / Time taken
= -7 meters / 3 seconds
= -7/3 meters per second
Interpreting the quotient, the rate of change of the bird's altitude can be described as -7/3 meters per second. The negative sign indicates that the bird is descending, while the absolute value of 7/3 indicates the magnitude of this descent.