AP Calculus ABmediummcq1 pt

Water enters a tank at a rate of 12+2t12+2t gallons per minute and leaves at a rate of 4+t4+t gallons per minute. What is the net change in the amount of water in the tank over the first 6 minutes?

A.108108 gallons
B.4242 gallons
C.6666 gallons
D.150150 gallons

Explanation

Core Concept

The net rate is (12+2t)(4+t)=8+t(12+2t)-(4+t)=8+t. The net change is 06(8+t)dt=[8t+t22]06=48+18=66\int_0^6(8+t)\,dt=[8t+\frac{t^2}{2}]_0^6=48+18=66 gallons.

Correct Answer

C6666 gallons

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