Question

The radius of a circular pond is increasing at a constant rate, which can be modeled by the function r(t) = 5t, where tis time in months. Thearea of the pond is modeled by the function A(1) = 1+?. The area of the pond with respect to time can be modeled by the compositionA(r(t).Which function represents the area with respect to time?OAA(r(t) = 5x52OBA(r(t) = 25m€2O cA(r(E) = 10x92O D.A(-(t)) = 51t?

Answer 1

Step-by-step explanation

We are asked to find the function that represents the area with respect to time A(r(t))

Given that

`\begin{gathered} r(t)=5t \\ \\ A(r)=\pi r^2 \end{gathered}`

what we will simply do will be to put in the value of r(t) into the equation of A(r)

Thus

`\begin{gathered} A(r)=[\pi*(5t)^2] \\ \\ A(r)=\pi*25t^2 \\ \\ A(r)=25\pi t^2 \end{gathered}`

Thus, the answer is option B