Question

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 in the bird’s altitude. Give your answer to the nearest hundredth and remember that the bird is descending

Answer 1

To find the rate of change in the bird's altitude, we can calculate the difference in altitude and then divide that by the time it takes to change that altitude.

1. **Initial altitude**: 10 meters
2. **Final altitude**: 3 meters
3. **Time taken**: 3 seconds

First, we calculate the change in altitude:

\[
\text{Change in altitude} = \text{Final altitude} - \text{Initial altitude} = 3 \text{ meters} - 10 \text{ meters} = -7 \text{ meters}
\]

Next, we find the rate of change of altitude by dividing the change in altitude by the time taken:

\[
\text{Rate of change} = \frac{\text{Change in altitude}}{\text{Time}} = \frac{-7 \text{ meters}}{3 \text{ seconds}} \approx -2.33 \text{ meters per second}
\]

Thus, the bird is descending at a rate of approximately **-2.33 meters per second** to the nearest hundredth.