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

Answer 1

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

$$\text{Rate}=\frac{\text{Change in altitude}}{\text{Time}}$$

1. Change in altitude: The balloon rises from 50 feet to 200 feet. So, the change in altitude is:

$$200\text{ feet}-50\text{ feet}=150\text{ feet}$$

2. Time: The time taken for this change is 7 minutes.

Now, plug these values into the formula:

$$\text{Rate}=\frac{150\text{ feet}}{7\text{ minutes}}\approx 21.43\text{ feet per minute}$$

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

As a rational number, you can represent this rate as:

$$\frac{150}{7}\text{ feet per minute}$$

So, the correct response is:

21.43 feet per minute.