At every moment from to hours

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

At every moment from t=0t=0 to t=5t=5 hours, a pump removes water from a tank at a constant rate of −3-3 liters per hour (the negative sign indicates removal). What is the sign of the net change in the amount of water in the tank during this time interval? (a) Positive, because removing a negative quantity yields a positive change.\text{Positive, because removing a negative quantity yields a positive change.} (b) Zero, because the rate is constant so its integral over time cancels out.\text{Zero, because the rate is constant so its integral over time cancels out.} (c) Negative, because water is being removed continuously.\text{Negative, because water is being removed continuously.} (d) Impossible to determine without knowing the initial volume of water.\text{Impossible to determine without knowing the initial volume of water.}

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