Algebra Investigation: Bacteria Growth, Colonies, and Factors

This algebra assignment delves into the mathematical modeling of bacterial growth. Part A focuses on developing an algebraic rule to describe bacterial population changes over time, using exponential equations and recurrence relations. It calculates bacterial populations after specific time intervals, including a calculation for two hours, and determines the time required for the colony to reach a million bacteria. Part B examines the relationship between colony size and the number of bacteria, colony morphology, and different replication rates. It also explores the impact of various growth-limiting factors on bacterial populations, such as environmental conditions, soil composition, oxygen availability, and nutrient limitations. The assignment provides a comprehensive analysis of bacterial growth dynamics, linking mathematical principles to biological phenomena, and includes references to relevant research and literature.

Algebra investigation

Table of Contents
Table of Contents........................................................................................................................................2
Part A.........................................................................................................................................................3
1. Algebraic rule that links the number of bacteria present at a specific point of time to the number of
bacteria present a minute prior.................................................................................................................3
2. Expression that is used in order to determine number of bacteria that would be present after t minutes
.................................................................................................................................................................3
3. Calculation of bacteria that would be present after 2 hours.................................................................3
Part B..........................................................................................................................................................4
a. Establishment of relationship between size of colony and the number of bacteria...............................4
b. Different rates of replication................................................................................................................4
c. Colonies of different sizes at the start..................................................................................................4
d. Effect of growth limiting factors..........................................................................................................5
REFERENCES..........................................................................................................................................7

Part A
1. Algebraic rule that links the number of bacteria present at a specific point of time to the
number of bacteria present a minute prior
Algebraic rule that has been used for the purpose of linking bacteria present at a specific point to
the number of bacteria present just before one minute is as follows:
It can be solve using an exponential equation
a(r)^n
A is constant which is 0, N is number of bacteria and thus the relation is a recurrence relation.
2. Expression that is used in order to determine number of bacteria that would be present after t
minutes
a(0) = 2
a(1) = 2(2)^2
a(2) = 2(2)^3
a(3) = 2(2)^4
a(4) = 2(2)^5
a(5) = 2(2)^6 = 64
3. Calculation of bacteria that would be present after 2 hours
a(2 hours =120 minutes) = 2(2) ^121
a(120)= 2(2) ^121 = 5.316911983139663e+36
4.Calculation of time that would be consumed by colony for reaching 1 million bacteria
18 minutes 30 seconds

Part B
a. Establishment of relationship between size of colony and the number of bacteria.
Bacteria usually expand on solid media such as colonies, a colony may be referred to as
visible mass of all those micro-organisms which originate from a single mother cell. Hence, a
colony constitutes a clone of bacteria all inherently alike (Andrade-Olivei and et.al., 2015). The
size of colony usually varies from large to tiny that is less than 1mm = punctiform(pin-point).
This measure would be based on a millimetre rule. In the identification of micro-organisms such
as fungi and bacteria; lot of emphasis is put on the way through which micro-organisms may
grow on or in the media (Khudoyberdiyev, Ladra and Omirov)
This activity will assist in identification of colony morphology. Colony morphology may be
defined as all those characteristics of a bacterium ion an agar plate which are cultural in nature.
However, there is no necessity to carry out colony morphology initially but it is essential at the
time of identification of bacterium. Characteristics of the colonies are very essential in order to
highlight the identify od the bacterium. Various species of bacteria can produce very different
colonies.
b. Different rates of replication
Degree to which bacteria may divide rapidly or slowly, depends completely upon the conditions
of growth. If the media is rich then the number of cells may double within 18 minutes. On the other hand,
if the nutrients are scare then the doubling time may rise up to 180 minutes. The cells of bacteria usually
accomplish this on the basis of the rate of re-initiation of replication. Re-initiation occurs at the similar
frequency of the cell doubling time (Rasouli and Davvaz, 2015).
c. Colonies of different sizes at the start
Colony morphology may be defined as a technique by which characteristics of individual colony
of bacteria grow on agar in a petri dish. There are various form of colonies Circular, Irregular,
Filamentous, Rhizoid.

Elevation of different size of colonies – Raised, Convex, Flat, Umbonate, Crateriform. It defines the side
view of a colony.
Margin of different colonies include Entire, Undulate Filiform, Curled and Lobate. Margin defines the
edge of the colony.
d. Effect of growth limiting factors
There are various factors limiting the growth of other different types of bacteria, these factors can
be defined as below –
1. Environmental factors – High temperature, soil acidity and drought can highly affect the growth of
bacteria.
2. Effect of clay – The amount and type of clay present in the soil can influence the soil matrix and hence
bacterial activity and survival (Rasoul and Davvaz, 2015).

3. Effect of oxygen – In acrobic nitrogen fixing organism for example – Azotobacter, nitrogen and
respiration fixation are alternative pathways of oxidation, the hydration to reduced substances are
eventually transferred initially in oxygen and then to nitrogen.
4. Effect of nutrient – Lack of carbon been having been assumed to be the most general limiting factor for
bacterial growth in soil, although there are report of limitation by other nutrients for example phosphorus
& nitrogen (Whitmore and Lamont, 2014).

REFERENCES
Books and Journals
Andrade-Oliveira, V. and et.al., 2015. Gut bacteria products prevent AKI induced by ischemia-
reperfusion. Journal of the American Society of Nephrology. 26(8). pp.1877-1888.
Khudoyberdiyev, A. K., Ladra, M. and Omirov, B. A., 2014. On solvable Leibniz algebras
whose nilradical is a direct sum of null-filiform algebras. Linear and Multilinear
Algebra. 62(9). pp.1220-1239.
Rasouli, S. and Davvaz, B., 2015. An investigation on Boolean prime filters in BL-algebras. Soft
Computing. 19(10). pp.2743-2750.
Whitmore, S. E. and Lamont, R. J., 2014. Oral bacteria and cancer. PLoS pathogens. 10(3).