Question

(5.5) A weather balloon is being filled at a rate of r(t) = 18(1 + 2t) 2 liters per second, starting with a volume of 0 liters at time t = 0. What is the volume of the balloon after 1 minute?

Answer 1

78 liters

Explanation:

The rate of change in volume is given by:

`r(t) =18(1+2t)^2\\r(t) = (4t^2+4t+1)*18\\r(t) = 72t^2+72t+18`

Integrating the expression above from t = 0 to t = 1 minute, gives us the final volume of the balloon after a minute:

`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`

The volume of the balloon after 1 minute is 78 liters.