Question

2025-2026 nc math 4 initial credit (approved for wmhs spr 26)
composition of functions and modeling
a marble dropped in still water will create circular ripples or waves. the radius of each circular wave will increase 4 centimeters per second. what is the circumference of the circle after ( t ) seconds?
( c(t) = 16pi t^2 )
( c(t) = pi t^2 )
( c(t) = 8pi t )
( c(t) = 2pi t )

Explanation:

Step1: Find radius after t seconds

The radius increases at 4 cm/s, so radius $r(t) = 4t$.

Step2: Apply circumference formula

Circumference $C = 2\pi r$. Substitute $r(t)$:
$C(t) = 2\pi \times 4t = 8\pi t$

Answer:

$C(t) = 8\pi t$