It is given that
A stone is thrown into a pond, A circular ripple spreads over the pond in such a way that the radius is increasing at a rate of 2.5 feet per second.
In one second the increment in radius is 2.5 feet
After t seconds, the increment in radius is given by
[tex]r(t)=2.5t[/tex]
The area of the circular ripple is
[tex]A(r)=\pi r^2[/tex]
[tex](A\circ r)(t)=A\lbrack r(t)\rbrack[/tex]
Substitute r(t)=2.5t, we get
[tex](A\circ r)(t)=A\lbrack2.5t\rbrack[/tex]
[tex]UseA(r)=\pi r^2,\text{ we get}[/tex]
[tex](A\circ r)(t)=\pi(2.5t)^2[/tex]
The required function is
[tex](A\circ r)(t)=6.25\pi t^2[/tex]
Hence the fourth option is correct.
