ABSTRACT
Thus, a plot of natural logarithm of population size against
time should yield a straight line, the slope of which should
equal k.
Eqs. 2 and 3 predict that growth will continue indefi-
nitely. However, growth results in the consumption of nutri-
ents and excretion of products from microbial metabolism.
Thus, after a certain time in a batch reactor (fermentor), the
growth rate decreases until population growth ceases alto-
gether. The growth curve becomes flat, indicating a station-
ary phase that is often followed by a decline indicating a
“death” phase (not shown). This may be due to depletion of
some essential nutrient in the medium (substrate limitation)
and/or accumulation of some autotoxic metabolic product in
the medium (toxin limitation). It is common to relate sub-
strate depletion to population growth through a stoichio-
metric relationship or yield constant:
