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

1 answer

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