Question

A pure culture in exponential growth has a bacterial concentration of 64x10
7 cells/ml. If the bacteria have a
doubling time of 1 hour, how long ago was the cell
concentration 8x107 cells/ml?

Answer 1

According to the question,

The no. of cells after time t (Nt )= 64 x 10^7 cells/ml

The initial no. of cells (N0) =8 x 10^7 cells

Therefore, n(the no of generations in time t)= (logNt-logN0)/0.301= {(log64x10^7)-(log8x10^7)}/0.301=3 generations

Since it is given that the doubling time is 1 hour, i.e. the bacteria doubles in number every after 1 hour.

And we have found out that to reach the final no. of cells in the culture the bacteria doubles 3 times, so, the time when the initial culture with 8x10^7 cells was setup = 3 hours before.