Bacterial Growth and how it
relates to Calculus
Bacteria are single cellular organisms that have been recognized on
their specific growth patterns, most commonly known as exponential
growth and decay. In this form of growth, the bacteria are doubling its
numbers every few minutes. Bacteria growth is documented in 4
specific phases: the lag phase, the log phase, the stationary phase, and
the death phase. Each of these phases represent a time in a group of
bacteria’s life cycle.
Lag Phase- At first, growth is fairly slow, even resources are far from
limited. The division of bacteria in this phase produces typically small
changes in the number of bacteria. As the bacteria near the end of the
lag phase, their numbers begin to grow much more quickly than what it
started.
Log Phase- This is the phase that bacteria grow the most. The resources
are still abundant, so the bacteria’s numbers will still be increasing. At
this point in the process, when the bacteria divide in two, the numbers
grow to extremely high levels. However, near the end of this phase,
growth shuts off in a sense.
Stationary Phase- In this phase, bacteria still grow, but at the same
time are decaying because of limited resources. At the peak level of this
phase, bacteria grow and decay at the exact opposite rates, making
total growth equal 0. As the bacteria move past this peak, they begin
losing more than they are gaining.
Death Phase- At this point in the cycle, bacteria begin dying instead of
producing new bacteria. Resources become very limited and toxic
waste build up causes death among the bacteria, until they are all dead.
Exponential growth in bacteria is represented by this formula:
Dn=kndt
Whereas Dn= the new number of bacteria, k is the constant (the
constant multiplied by the time interval must always equal 2), n is the
number of bacteria from the last time interval, and dt is the time
interval at which the bacteria grows.
In example, I will demonstrate this formula when bacteria double every
20 minutes, and bacteria numbers are at 128 previously.
Dn=kndt
Dn=(1/10)(128)(20)
Dn=2(128)
_____________
Dn=256
_____________
Future Use of Bacterial Growth
The future application and future use of bacterial growth varies
depending on what field it will be applied too. In medicine, it is possible
to learn the optimal conditions that bacteria can breed. This could be
greatly beneficial to mankind because there are some bacteria that are
not harmful to the body and instead of crippling the body they typically
help fortify the body’s natural defense. If bred, it is possible to collect
abundance amounts of helpful bacteria for sick or weaker individuals.
In Biology, there have been genetic modifications of E. Coli bacteria.
While the bacteria is normally disregarded because of its poisoning to
food, a scientists were able to modify it to produce hydrogen 140 times
quicker then natural processes. With bacterial growth it is possible to
optimize this strain of E. Coli to grow efficiently and then help produce
massive amounts of hydrogen.
Sources
http://www.sciencedaily.com/releases/2008/01/080129170709.htm
http://www.cellsalive.com/ecoli.htm
http://www.newton.dep.anl.gov/askasci/mole00/mole00405.htm
.