MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A storage tank initially contains 350 liters of water. During the next 10 minutes, water flows in and out of the tank at a rate modeled (in liters per minute) by
v(t)=5t−30,0≤t≤10,
where positive values of v(t) represent inflow and negative values represent outflow.
(a) Determine the exact net change in the volume of water in the tank during the 10-minute interval. Include units in your answer.
(b) At what time t, with 0<t<10, does the tank contain exactly its initial volume of 350 liters again? Justify your answer algebraically.
(c) Interpret the integral ∫0t∣v(u)∣du in this context and explain how it differs from the expression calculated in part (a). No numerical evaluation is required.