Step 1 :The problem is asking for the total amount of water that flows from the tank during the first 30 minutes. This can be found by integrating the rate function from 0 to 30. The integral of a rate function over an interval gives the total amount of change over that interval. In this case, the rate function is \(r(t) = 200 - 4t\), and we are integrating from 0 to 30.
Step 2 :Let's denote time as \(t\) and the rate of water flow as \(r\), which is given by \(r = 200 - 4*t\).
Step 3 :By integrating the rate function from 0 to 30, we find that the total amount of water that flows from the tank during the first 30 minutes is 4200 liters.
Step 4 :Final Answer: The total amount of water that flows from the tank during the first 30 minutes is \(\boxed{4200}\) liters.