Question

while being deflated, a hot - air balloon has 900 cubic meters of air. the volume of the air in cubic meters, v, is a function of time in minutes, x. you can write an equation to represent the function. describe the rate of change. the rate of change is? because the amount of air in the balloon? over time.

Explanation:

Step1: Assume constant deflation rate

Let's assume the balloon deflates at a constant rate. Suppose it takes \( t \) minutes to deflate completely (we need more info, but let's generalize). The volume \( V \) as a function of time \( x \) (in minutes) would be \( V(x)=900 - rx \), where \( r \) is the rate of change (deflation rate, negative since volume decreases).

Step2: Analyze rate of change

The rate of change (slope of the linear function) is negative because the volume of air in the balloon is decreasing over time. So the rate of change is negative, and the volume is decreasing over time.

Answer:

The rate of change is negative because the amount of air in the balloon is decreasing over time. (Note: To fully solve, we need the time taken to deflate, e.g., if it deflates in \( m \) minutes, rate \( r = \frac{900}{m} \) cubic meters per minute, negative as volume decreases.)