Question 18.AP.5: Bacterial Growth In biological applications concerned with p...
Bacterial Growth
In biological applications concerned with population growth, an equation is used that is similar to the exponential equations encountered in the analysis of RC circuits. Applied to a number of bacteria, this equation is
N_{f}=N_{i}{}{2^{n}}
where { N}_{f} is the number of bacteria present after n doubling times, { N}_{i} is the number present initially, and n is the number of growth cycles or doubling times. Doubling times vary according to the organism. The doubling time for the bacteria responsible for leprosy is about 30 days, and that for the salmonella bacteria responsible for food poisoning is about 20 minutes. Suppose only 10 salmonella bacteria find their way onto a turkey leg after your Thanksgiving meal. Four hours later you come back for a midnight snack. How many bacteria are present now?
The number of doubling times is 240 min/20 min = 12. Thus,
N_{f}=\,N_{i}2^{n}=\,(10\mathrm{~bacteria})({2^{12}})\,=\,40\,\ 960\mathrm{~bacteria}
So your system will have to deal with an invading host of about 41 000 bacteria, which are going to continue to double in a very promising environment.