A bacterial culture with a starting density of 1×10^3 cells/ml is incubated in liquid nutrient broth. If the bacteria have both a lag time and a generation time of 10 minutes, what will the cell density be at 30 minutes?

To determine the cell density at 30 minutes, we need to consider both the lag time and the generation time of the bacteria. In this scenario, the starting density is 1×10^3 cells/ml, the lag time is 10 minutes, and the generation time is also 10 minutes.

Initially, during the first 10 minutes (the lag phase), the bacteria do not divide; they are instead adapting to their environment and preparing for growth. Therefore, after the first 10 minutes, the cell density remains at 1×10^3 cells/ml.

Following the lag phase, there is a subsequent growth phase where the bacteria begin to divide. Since the generation time is 10 minutes, we can expect a doubling of the bacterial population at each 10-minute interval thereafter. Given that we have a total duration of 30 minutes, this time can be divided into three segments of 10 minutes each: the first segment being the lag phase and the next two segments corresponding to two rounds of division.

At the end of the first 10 minutes, the cell density remains at 1×10^3 cells/ml. At the end of the second period (20 minutes), the population doubles to 2×10^3 cells