Question
The hot air balloon rises from 50 feet above the ground to 200 feet above the ground in 7 minutes. What is the rate of change in the balloons altitude?
Answers
GPT-4o mini
To find the rate of change in the balloon's altitude, we can follow these steps:
1. Determine the change in altitude:
\[
\text{Change in altitude} = \text{Final altitude} - \text{Initial altitude} = 200 \text{ ft} - 50 \text{ ft} = 150 \text{ ft}
\]
2. Determine the time taken for this change:
\[
\text{Time} = 7 \text{ minutes}
\]
3. Calculate the rate of change in altitude:
\[
\text{Rate of change} = \frac{\text{Change in altitude}}{\text{Time}} = \frac{150 \text{ ft}}{7 \text{ min}} \approx 21.43 \text{ ft/min}
\]
Thus, the rate of change in the balloon's altitude is approximately **21.43 feet per minute**.
1. Determine the change in altitude:
\[
\text{Change in altitude} = \text{Final altitude} - \text{Initial altitude} = 200 \text{ ft} - 50 \text{ ft} = 150 \text{ ft}
\]
2. Determine the time taken for this change:
\[
\text{Time} = 7 \text{ minutes}
\]
3. Calculate the rate of change in altitude:
\[
\text{Rate of change} = \frac{\text{Change in altitude}}{\text{Time}} = \frac{150 \text{ ft}}{7 \text{ min}} \approx 21.43 \text{ ft/min}
\]
Thus, the rate of change in the balloon's altitude is approximately **21.43 feet per minute**.