Question

A hot air balloon can hold 90,000 cubic feet of air. It is being inflated at a rate of 6,000 cubic feet per minute. The total cubic feet of air a(t) is a function of the in minutes t. a. Identify the independent and dependent variables. b. What values of the domain and range make sense for this situation? Explain. c. Write a function to represent the total amount of air. Then determine the total amount of air in 6 minutes.

Answer 1

a. The independent variable is the variable whose variation does not depend on that of another, it is often denoted by x.
In our case independent variable is time in minutes
The dependent variable is the volume of air in the balloon.

b] The domain of the of this situation is:
[0≤t≤15]
this is because t will take 15 minutes for the balloon to get filled.

The range of the situation will be:
[0≤a(t)≤90000]

c]The function that represents this situation is a linear function given by:
y=ax+b
where:
a=rate/slope
b= initial amount of air in the balloon=0
Thus our function will be:
a(t)=6000t

d]
The total amount of air in the balloon after 6 minutes will be given by:
from
a(t)=6000t
a(6)=6000(6)
a(6)=36000 cubic feet