The population \( P(t) \) of a culture of the bacterium Pseudomonas aeruginosa is given by \( P(t)=-1683 t^{2}+83,000 t+10,000 \), where \( t \) is the time in hours since the culture was started. Part 1 of 2 a) Determine the time at which the population is at a maximum. Round to the nearest hour. The population is at a maximum approximately __ hours after the culture was started. Part 2 of 2 b) Determine the maximum population. Round to the nearest thousand. The maximum population is approximately __
