Answer:
78 liters
Step-by-step explanation:
The rate of change in volume is given by:
[tex]r(t) =18(1+2t)^2\\r(t) = (4t^2+4t+1)*18\\r(t) = 72t^2+72t+18[/tex]
Integrating the expression above from t = 0 to t = 1 minute, gives us the final volume of the balloon after a minute:
[tex]V=\int\limits^1_0 { (72t^2+72t+18}) \, dt \\V=(24t^3+36t^2+18t+c)|_0^1\\V=24+36+18+c-c=78\ liters[/tex]
The volume of the balloon after 1 minute is 78 liters.
