A chemist is carrying out laboratory experiments to verify the operation of a new pharmacy on a bacterium. The model makes a count of the number of bacteria present in the sample with respect to the time in hours, from which the drug is supplied and is: N(t) = 10t³ - 255t² + 1800t + 1000 a) According to the model presented, how many bacteria were counted before administering the drug? b) How long after the drug is administered do the first signs of its effectiveness appear? That is, at what point do bacteria begin to decline? c) At what time does the drug show its best result? That is, at what time does it maximize and reach the lowest number of bacteria? d) If the drug must be administered again as soon as it begins to stop working, how long after should a new dose be administered?

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