Answer:
(a) [tex]V=2+0.5t[/tex]
(b) It takes 26 seconds to completely fill the balloon.
Step-by-step 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
⇒ [tex]V=V_0+rt[/tex]
⇒ [tex]V=2+0.5t[/tex]
Therefore, the linear function 'V' that models the volume of hydrogen in the balloon at any time 't' is [tex]V=2+0.5t[/tex]
(b)
Given:
Balloon has a capacity of 15 ft³. This means the total volume of hydrogen that can be filled is 15 ft³.
So, [tex]V=15\ ft^3[/tex]
Plugging 'V' value in the above equation and solving for 't', we have:
[tex]15=2+0.5t\\\\0.5t=15-2\\\\0.5t=13\\\\t=\frac{13}{0.5}=26\ s[/tex]
Therefore, it takes 26 seconds to completely fill the balloon.
