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CHAPTER 3

Factors Affecting the Growth and

Survival of Micro-organisms in Foods

3.1 MICROBIAL GROWTH

Microbial growth is an autocatalytic process: no growth will occur
without the presence of at least one viable cell and the rate of growth
will increase with the amount of viable biomass present. This can be
represented mathematically by the expression:

dx=dt¼mx ð 3 : 1 Þ

where dx/dtis the rate of change of biomass, or numbersxwith timet,
andmis a constant known as the specific growth rate.
The same exponential growth rule applies to filamentous fungi which
grow by hyphal extension and branching since the rate of branching
normally increases with hyphal length.
Integration of Equation (3.1) gives:

x¼x 0 emt ð 3 : 2 Þ

or, taking natural logarithms and re-arranging:

lnðx=x 0 Þ¼mt ð 3 : 3 Þ

wherex 0 is the biomass present whent¼0.
The doubling or generation time of an organismtcan be obtained by
substitutingx¼ 2 x 0 in Equation 3.3. Thus:

t¼ln 2=m¼ 0 : 693 =m ð 3 : 4 Þ

An alternative way of representing exponential growth in terms of the
doubling time is:

x¼x 02 t=t ð 3 : 5 Þ