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.

Question

Mathematics

Abigayle Rivas

24 March, 08:58

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.

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Brewster · 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]