At 4:00 p.m.a closed flask of sterile broth is inoculated with 10,000 cells.The lag phase lasts 1 hour.At 9:00 p.m.the culture enters stationary phase with a population of 65 million cells.At what time is the population half maximal?

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The population is half maximal when it reaches half of 65 million, which is 32.5 million. The exponential phase of growth occurs between the end of the lag phase (5:00 p.m.) and the beginning of the stationary phase (9:00 p.m.). Since the population increases exponentially during this time, to find when the population is half of its maximum (32.5 million), we look for the midpoint in time between the start and end of this phase. Given the exponential growth, the population would reach half its maximum size just before it stops growing. Since the stationary phase starts at 9:00 p.m., the population would be half maximal shortly before this, at 8:40 p.m.

At 4:00 PM