Question

A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius (in meters) of the outer ripple is given by r(t) =0.2t, where t is the time in seconds after the pebble strikes the water. The area of the circle is given by the function A(r) = π . Find and interpret (Aₒr)(t).

Answer 1

Since A(r)=π is constant, A(r) is also constant.
Now, if you meant to say that A(r) = πr^2 then we have
(A◦r)(t) = A(r(t)) = π(0.2t)^2 = 0.04πt^2