A bird is flying at an average altitude of 10 m above the ground after 3 seconds it settles on a branch that is 3 m above the ground interpret the quotient to describe the rate of change in the bird's altitude give your answers to the nearest hundredth and remember that the bird is descending the quotient that best represents the rate of change in the birds altitude is meters seconds

Answer 1

To determine the rate of change in the bird's altitude as it descends from an average altitude of 10 meters to a branch that is 3 meters above the ground over a time period of 3 seconds, we can use the formula for the average rate of change.

The formula for the average rate of change is:

\[ \text{Rate of change} = \frac{\text{Change in altitude}}{\text{Time period}} \]

1. Calculate the change in altitude:

   • Initial altitude = 10 m
   • Final altitude = 3 m
   • Change in altitude = Final altitude - Initial altitude = 3 m - 10 m = -7 m

2. Time period:

   • Time = 3 seconds

3. Substituting into the formula:

\[ \text{Rate of change} = \frac{-7 \text{ m}}{3 \text{ s}} \approx -2.33 \text{ m/s} \]

Thus, the quotient that best represents the rate of change in the bird's altitude, rounded to the nearest hundredth, is approximately -2.33 meters per second. This negative value reflects the fact that the bird is descending.