Question

During exponential phase in batch culture, the growth rate of a culture is proportional to the concentration of cells present. When Streptococcus bacteria are cultured in milk, the concentration of cells doubles in 50 min. If this rate of growth is maintained for 8h, what is the final concentration of cells relative to the inoculum level? 

Answer 1

total time of growth = 8 hours

doubling time= 50 minutes

$0\ min \to50\ min \to 1\ hr\ 40\ min \to 2\ hr\ 30\ min\to 3\ hr\ 20\ min \to 4\ hr\ 10\ min\to 5\ hr \to 5\ hr\ 50\ min\to6\ hr\ 40\ min\to 7\ hr\ 30\ min\to 8\ hr\ 20\ min$

Assuming that the concentration of the culture at 0 minutes is x cells/cm³

Just before 8 hours, there are 10 divisions.

$\therefore$ the concentration of the culture increases by $x × 2^{10}$, which is equivalent to 1024x.