A Pebble Is Dropped into a Calm Pond, Causing Ripples $r ( t ) = 0.5 t$

Multiple Choice

A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius (in feet) of the outermost ripple is given by $r ( t ) = 0.5 t$ where $t$ is time in seconds after the pebble strikes the water. The area of the outermost circle is given by the function $A ( r ) = \pi r ^ { 2 }.$ Find and interpret $( A \circ r ) ( t ) .$

A) $( A \circ r ) ( t ) = \pi t ^ { 2 };$ $A \circ r$ represents the radius of the circle at time $t.$
B) $( A \circ r ) ( t ) = 0.5 \pi t ^ { 2 };$ $A \circ r$ represents the radius of the circle at time $t.$
C) $( A \circ r ) ( t ) = 0.25 \pi t ^ { 2 };$ $A \circ r$ represents the radius of the circle at time $t.$
D) $( A \circ r ) ( t ) = 0.25 \pi t ^ { 2 };$ $A \circ r$ represents the area of the circle at time $t.$
E) $( A \circ r ) ( t ) = 0.5 \pi t^ { 2 };$ $A \circ r$ represents the area of the circle at time $t.$