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

question 18

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 \(t.\)

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