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?

Question

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
-21.43 feet per minute

Answer 1

To determine the rate of change in the balloon’s altitude, we can use the formula for the rate of change, which is:

\[ \text{Rate of change} = \frac{\text{Change in altitude}}{\text{Change in time}} \]

1. Calculate the change in altitude:

   • Initial altitude = 50 feet
   • Final altitude = 200 feet
   • Change in altitude = Final altitude - Initial altitude = 200 feet - 50 feet = 150 feet

2. Calculate the change in time:

   • The time taken = 7 minutes

3. Now, calculate the rate of change: \[ \text{Rate of change} = \frac{150 \text{ feet}}{7 \text{ minutes}} \approx 21.43 \text{ feet per minute} \]

So, the rate of change in the balloon’s altitude is approximately 21.43 feet per minute.

This rate can be represented as a rational number by writing it as a fraction:

\[ \frac{150}{7} \text{ feet per minute} \]

Hence, the correct response is:

21.43 feet per minute.