MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
Crude oil is leaking from a tanker, forming a single uniform circular slick on the surface of calm water. The area A (in m2) of the slick increases at a constant rate of 300 m2/min. At a particular moment the radius of the slick is 20 m.
(a) Calculate the instantaneous rate of change of the radius of the slick at that moment. State the units of your answer.
(b) Assuming the area continues to increase at the same constant rate of 300 m2/min, determine the amount of time, in minutes, required for the radius to grow from 20 m to 25 m. Show all analytical work leading to your result.