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 balloon’s altitude?

How can this rate be represented as a rational number?

(1 point)
Responses

4 feet per minute
4 feet per minute

21.43 feet per minute
21.43 feet per minute

28.6 feet per minute
28.6 feet per minute

-21.43 feet per minute

Answer 1

To determine the rate of change in the balloon’s altitude, we first find the total change in altitude and then divide that by the time taken to make that change.

1. **Calculate the change in altitude:**
\[
\text{Change in altitude} = \text{Final altitude} - \text{Initial altitude} = 200 \text{ feet} - 50 \text{ feet} = 150 \text{ feet}
\]

2. **Calculate the time taken:**
\[
\text{Time taken} = 7 \text{ minutes}
\]

3. **Calculate the rate of change:**
\[
\text{Rate of change} = \frac{\text{Change in altitude}}{\text{Time taken}} = \frac{150 \text{ feet}}{7 \text{ minutes}} \approx 21.43 \text{ feet per minute}
\]

Thus, the rate of change in the balloon's altitude is approximately **21.43 feet per minute**.

This can also be represented as a rational number because \( 150/7 \) is a fraction, which is a form of a rational number.

**Correct Response:**
21.43 feet per minute