A Pebble Is Dropped into a Calm Pond, Causing Ripples $r ( t ) = 0.2 t$

question 164

Multiple Choice

A pebble is dropped into a calm pond, causing ripples in the form of concentric circles.The radius (in feet) of the outer ripple is $r ( t ) = 0.2 t$ , where t is the time in seconds after the pebble strikes the water.The area of the circle is given by the function $A ( r ) = \pi r ^ { 2 }$ .Find and interpret $( A \circ r ) ( t )$ .

• A) \(( A \circ r ) ( t ) = 0.2 \pi t\) ; \(( A \circ r ) ( t )\) represents the area of the circle at time t.
• B) \(( A \circ r ) ( t ) = 0.2 \pi t ^ { 2 }\) ; \(( A \circ r ) ( t )\) represents the area of the circle at time t.
• C) \(( A \circ r ) ( t ) = 0.04 \pi t\) ; \(( A \circ r ) ( t )\) represents the area of the circle at time t.
• D) \(( A \circ r ) ( t ) = 0.04 \pi t ^ { 2 }\) ; \(( A \circ r ) ( t )\) represents the area of the circle at time t.
• E) \(( A \circ r ) ( t ) = 0.04 \pi t ^ { 3 }\) ; \(( A \circ r ) ( t )\) represents the area of the circle at time t.

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