The population P(t) of a culture of the bacterium Pseudomonas aeruginosa is given by P(t)=-1687t2 +83,000t+10,000, where it is

Question

The population P(t) of a culture of the bacterium Pseudomonas aeruginosa is given by P(t)=-1687t2 +83,000t+10,000, where it is the time in hours since the culture was started.

(a) Determine the time at which the population is at a maximum. Round to the nearest hour.

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