Answer:
4,200 liters
Step-by-step explanation:
The flow rate is given by:
[tex]r(t) = 200 - 4t[/tex]
Integrating the flow rate expression from t=0 to t=30 minutes, yields the total volume that flows out of the tank during that period:
[tex]\int\limits^{30}_0 {r(t)} = \int\limits^{30}_0 {(200 - 4t} )\, dt \\V=(200t - 2t^2)|_0^{30}\\V= (200*30 -2*30^2)-(200*0 -2*0^2)\\V=4,200\ liters[/tex]
4,200 liters of water flow from the tank during the first 30 minutes.
