Question

Weather balloons are filled with hydrogen and released at various sites to measure and transmit data about conditions such as air pressure and temperature. A weather balloon is filled with hydrogen at the rate of0.5ft3/s. Initially, the balloon contains2ft3of hydrogen. (a) Find a linear function V that models the volume of hydrogen in the balloon at any time t. (b) If the balloon has a capacity of15ft3, how long does it take to completely fill the balloon?

Answer 1

(a)
`V=2+0.5t`

(b) It takes 26 seconds to completely fill the balloon.

Explanation:

Let the time for which balloon is filled be 't' seconds.

(a)

Given:

Rate of filling (r) = 0.5 ft³/s

Initial volume of hydrogen in the balloon (V₀) = 2 ft³

The filling of hydrogen is a linear function of time.

So, Volume of hydrogen filled in the balloon at any time 't' is given as:

Volume = Initial volume + Rate of fill × time taken

⇒
`V=V_0+rt`

⇒
`V=2+0.5t`

Therefore, the linear function 'V' that models the volume of hydrogen in the balloon at any time 't' is
`V=2+0.5t`

(b)

Given:

Balloon has a capacity of 15 ft³. This means the total volume of hydrogen that can be filled is 15 ft³.

So,
`V=15\ ft^3`

Plugging 'V' value in the above equation and solving for 't', we have:

`15=2+0.5t\\\\0.5t=15-2\\\\0.5t=13\\\\t=(13)/(0.5)=26\ s`

Therefore, it takes 26 seconds to completely fill the balloon.