Final answer:
After 6 generations and 3 hours, the culture's cell number would be 2.048∙10⁴ cells/ml, and by 13 hours, the culture would likely have reached the stationary phase, where growth ceases and cell numbers plateau.
Step-by-step explanation:
The number of cells added to the culture was 3.2∙10² cells/ml. To determine the cell number after an estimated 6 generations of growth, considering that cells are doubling at each generation, we use the exponential growth formula 2⁹, where n is the number of generations. Assuming a generation time of 30 minutes, six generations would occur after 3 hours. The initial cell count would be multiplied by 2⁹ (or 64) to give us the final cell count. In this case, the final cell count would be 3.2∙10² cells/ml multiplied by 64, which equals 2.048∙10⁴ cells/ml.
As for the growth curve phase, we can infer that after 13 hours and 6 generations, the culture would likely reach the stationary phase. This is the phase where growth ceases or slows significantly because of factors such as nutrient depletion, waste accumulation, or limited space, which typically leads to a plateau in cell numbers. In the stationary phase, the number of new cells produced is roughly equal to the number of cells dying.