Question

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

Answer:

The volume after 1 minute is 5314680 liters.

Step-by-step explanation:

We are given the following in the question:

$\dfrac{dV}{dt}=r(t) = 18(1 + 2t)^2$

where r(t) is the rate in liters per second starting with a volume of 0 liters at time t = 0.

We have to find the volume of balloon after 1 minute.

We evaluate it in the following manner:

t = 60 and t = 0

$V =\displaystyle\int^{60}_0 18(1 + 2t)^2~dt\\\\V = 18 \bigg [ \dfrac{(1+2t)^3}{(3)(2)}\bigg ]^{60}_0\\\\V = 3[(1+2(60))^3-(1+2(0))^3]\\V = 3(1771560)\\V = 5314680$

Thus, the volume after 1 minute is 5314680 liters.