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.

Answer 1

wrong

Answer 2

To determine the rate of change in the bird's altitude, we start by calculating the initial altitude and the final altitude at the given times.

- The initial altitude of the bird is 10 meters.
- After 3 seconds, the bird settles at an altitude of 3 meters.

Next, we find the change in altitude:
\[
\text{Change in altitude} = \text{Final altitude} - \text{Initial altitude} = 3\, \text{meters} - 10\, \text{meters} = -7\, \text{meters}
\]

The negative sign indicates that the bird is descending.

Now, we need to calculate the rate of change. The rate of change is given by the change in altitude divided by the time it took for that change:
\[
\text{Rate of change} = \frac{\text{Change in altitude}}{\text{Time}} = \frac{-7\, \text{meters}}{3\, \text{seconds}} \approx -2.3333\, \text{meters per second}
\]

Rounding this to the nearest hundredth gives us:
\[
\text{Rate of change} \approx -2.33\, \text{meters per second}
\]

Thus, the interpretation is that the bird's altitude is decreasing at a rate of approximately 2.33 meters per second.

Answer 3

I apologize for any confusion in my previous response. Let’s go through the calculations again step-by-step to determine the rate of change in the bird’s altitude accurately.

1. **Initial Altitude**: The bird’s altitude is 10 meters.
2. **Final Altitude**: After 3 seconds, the bird settles at an altitude of 3 meters.
3. **Change in Altitude**:
\[
\text{Change in altitude} = \text{Final altitude} - \text{Initial altitude} = 3\, \text{meters} - 10\, \text{meters} = -7\, \text{meters}
\]

4. **Time Interval**: The time taken for this change is 3 seconds.
5. **Rate of Change**:
\[
\text{Rate of change} = \frac{\text{Change in altitude}}{\text{Time}} = \frac{-7\, \text{meters}}{3\, \text{seconds}} \approx -2.3333\, \text{meters per second}
\]

6. **Rounding to the Nearest Hundredth**:
\[
-2.3333 \text{ rounds to } -2.33
\]

This means the bird is descending at a rate of approximately **-2.33 meters per second**.

If you have further information or a specific point of contention, please let me know!