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CalculusMediumThe Derivative

The Derivative · Medium problem

Two bacterial colonies have sizes A(t)=2t3A(t)=2t^3 (thousand cells) and B(t)=24tB(t)=24t (thousand cells), for t≥0t\ge0 in hours. At what time t>0t>0 are the two colonies growing at exactly the same rate (that is, A′(t)=B′(t)A'(t)=B'(t))?