Answer
(a) $g(t)=60t$
(b) $f(r)=\pi r^2$
(c) $f∘g=3600\pi t^2$
This simply represents the area of circle for given $t$ seconds.
Work Step by Step
(a) According to the information we are given, every $t$ second the circular ripple travels $60cm$, so we can simply write a function to model the radius of this circle for given $t$ second.
$g(t)=60t$
Where $g(x)$ represents radius in $cm$ and $t$ time in $sec$.
(b) As we found out previously in (a) radius for given $t$ sec is $60t$. (Which we will need to calculate area of the circle for any given time).
In general Area of circle is equal to $\pi r^2$, so we can write:
$f(r)=\pi r^2$
(c) $f∘g=f(g(t))=f(60t)=\pi \times (60t)^2=3600\pi t^2$
$f∘g=3600\pi t^2$
This simply represents the area of circle for given $t$ seconds.