Question

Antonio drops a glass marble into a pond and creates ripples that form concentric circles on the surface of the water. The radius of the circle, r, in centimeters is given by the function , where t is the time in seconds that the ripples move outward from the center of the circle. Find the function A(t) that represents the area, A, of the expanding circle in t seconds.

Answer 1

The function given is r(t) = 1 + 4t, where r is the radius in centimeters and t is time in seconds.

So, use the formula of the area: area = π (radius)^2

A(t) = π [r(t) ] ^2

A(t) = π [1 + 4t ]^2 = π [1 + 8t + 16t^2 ]

Answer: π [ 16t^2 + 8t + 1]