In the exponential phase, the microbial growth rate (dN/dt) is given by the foll
ID: 72338 • Letter: I
Question
In the exponential phase, the microbial growth rate (dN/dt) is given by the following equation:
N k dt dN
Where, k is kinetic constant (time-1). N is number of microbial cells (# of cells), and t is the time during exponential phase (time)
(i) (5 points) Derive an equation to calculate N by assuming the following initial and final conditions: N = cell number @ time t; N0 = cell number @ time t = 0.
(ii) (5 points) Determine the mean holding time (hr) required to sterilize swine flu virus to N/N0 = 10-10 if the reaction rate constant is k = 0.7 min-1 in a batch sterilizer operating at 125°C. Here, N = number of virus at time = t; and N0 is the number of virus at time = 0.
Explanation / Answer
Microbial growth follows the following growth pattern
Cells divide, one cell give rise to 2 daughter cells
The number of cells after time t depends on the number of cells at the beginning of the culture(time =0) and generation time or doubling time of the bacteria
Substrates + cells extracellular products + more cells
This can be represented by the differential equation given below:
Where K is kinetic constant
Integrating equation 1, we get