QuestionFind the function $(A \circ r)(t)$ if the radius $r(t)$ of ripples in a pond is known, where $A(r)=\pi r^{2}$.

Studdy Solution
Substitute $r(t)$ into $A(r)$.
$$(A \circ r)(t) = A(r(t)) = \pi (r(t))^{2}$$So, the function $(A \circ r)(t)$ is $\pi (r(t))^{2}$.