Why does bacterial growth look like exponential growth in practice?
The answer is because bacterial growth is not completely synchronized. Some cells divide in fewer than 3 hours; while others will take a little longer to divide. Even if you start a culture with a single cell, synchronicity will be maintained only through a few cell divisions. A single cell will divide at a discrete point in time, and the resulting 2 cells will divide at ABOUT the same time, and the resulting 4 will again divide at ABOUT the same time. As the population grows, the individual nature of cells will result in a smoothing of the division process. This smoothing yields an exponential growth curve, and allows us to use exponential functions to make calculations that predict bacterial growth. So, while exponential growth might not be the perfect model of bacterial growth by binary fission, it is the appropriate model to use given experimental reality.