Science:Math Exam Resources/Courses/MATH110/December 2014/Question 09 (a)/Statement

When a pebble is thrown into a pond, circular ripples form on the water surface. Suppose ${\textstyle r(t)}$ is the radius, in centimetres, of one such ripple at ${\textstyle t}$ minutes after the pebble falls into the water, and ${\textstyle A(r)}$ is the surface area of a ripple of radius ${\textstyle r}$.

(a) Which of the following statements best explains the meaning of the composite function ${\textstyle A(r(t))}$?

(i) The radius of the ripple, in centimetres, at time ${\textstyle t}$ minutes.

(ii) The area of the ripple, in square centimetres, of radius ${\textstyle r}$ centimetres.

(iii) The area of the ripple, in square centimetres, at time ${\textstyle t}$ minutes.

(iv) The function ${\textstyle f}$ of the minutes and the area.

(v) The product of the area of the ripple, in square centimetres, by the ripple’s radius at time ${\textstyle t}$ minutes.