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Interpreting Derivatives of a Rate Function

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For time t≥0t \geq 0 hours, A(t)A(t) represents the rate, in square meters per hour, at which the area of an oil slick is expanding. Consider the following scenarios at t=3t=3:

I. A′(3)>0A'(3) > 0 and A(3)>0A(3) > 0

II. A′(3)<0A'(3) < 0 and A(3)>0A(3) > 0

III. A′(3)=0A'(3) = 0 and A(3)>0A(3) > 0

Which scenario describes the condition that at t=3t=3 hours, the area of the oil slick is increasing, but its rate of expansion is decreasing?

A

Scenario III only

B

Scenario I only

C

Both Scenarios I and III

D

Scenario II only

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