Question

A rain drop hitting a lake makes a circular ripple. If the radius, in inches, grows as a function of time in minutes according to r(t)=15√t+2, find the area of the ripple as a function of time. Find the area of the ripple at t=2 .

Answer 1

FiThe radius, in inches, grows as a function of time in minutes according to:

`r(t)=15√(t+2)`

We know that the area of a circle is given by:

`A=\pi r^2`

Where r is the radius of the circle. Then, using r(t) in this equation:

`\begin{gathered} A(t)=\pi\cdot\lbrack r(t)\rbrack^2=\pi\lbrack15√(t+2)\rbrack^2 \\ \\ \therefore A(t)=225\pi(t+2) \end{gathered}`

Finally, we evaluate this function for t = 2:

`\begin{gathered} A(2)=225\pi(2+2)=225\pi(4) \\ \\ \therefore A(2)=900\pi\text{ in}^2 \end{gathered}`