A rectangular swimming pool has length metres and width metres
MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A rectangular swimming pool has length x(t) metres and width y(t) metres.
Because of ground movement, the width is decreasing at 0.20m h−1 while the length is increasing.
At a certain instant the dimensions are 30m×20m and the perimeter is known to be increasing steadily at 0.05km h−1.
(a) Express the given rate of change of perimeter in metres per hour.
(b) Calculate the rate at which the length is changing at that instant.
(c) Determine the percentage change in the area of the pool per hour at the same instant, stating clearly whether the area is increasing or decreasing.