Question

How much water flows out of the tank during the first 2 minutes if a valve in a full 6000 gallon water tank is slowly opening and water flows out of the tank through the valve.at a rate in gallons per hour is given by the function `f(t) = 300*t^2` where t is in minutes?

Answer 1

I would integrate your function between t=0 (the start) and t=2 min.
`int_0^2(300t^2)dt=300[t^3/3]_0^2=800 gallons`
Here I used your function as rate of gallons per minutes.