At time t = 0, a storage tank is empty and begins filling with water. For t > 0 hours, the depth of the water in the tank is increasing at a rate of W(t) feet per hour. Which of the following is the best interpretation of the statement W'(2) > 3 ? (A) Two hours after the tank begins filling with water, the depth of the water is increasing at a rate greater than 3 feet per hour. (B) Over the first two hours after the tank begins filling with water, the depth of the water is always increasing at a rate greater than 3 feet per hour. (C) Two hours after the tank begins filling with water, the rate at which the depth of the water is rising is increasing at a rate greater than 3 feet per hour per hour. (D) Over the first two hours after the tank begins filling with water, the rate at which the depth of the water is rising is always increasing at a rate greater than 3 feet per hour per hour.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.