Question

The radius of a circular pond is increasing at a constant rate, which can be modeled by the function , where t is time in months. The area of the pond is modeled by the function . The area of the pond with respect to time can be modeled by the composition . Which function represents the area with respect to time? A. B. C. D.

Answer 1

Answer:

B. A(r(t)) = 25πt²

Step-by-step explanation:

Find the completed question below

The radius of a circular pond is increasing at a constant rate, which can be modeled by the function r(t) = 5t where t is time in months. The area of the pond is modeled by the function A(r) = πr². The area of the pond with respect to time can be modeled by the composition . Which function represents the area with respect to time? A. B. C. D.

Given

A(t) = πr²

r(t) = 5t

We are to evaluate the composite expression A(r(t))

A(r(t)) = A(5t)

To get A(5t), we will replace r in A(t) with 5t and simplify as shown

A(5t) = π(5t)²

A(5t) = π(25t²)

A(5t) = 25πt²

A(r(t)) = 25πt²

Hence the composite expression A(r(t)) is 25πt²

Option B is correct.