Bacterial Growth: Algebraic Rules, Colony Analysis, and Factors

This homework assignment delves into the algebraic modeling of bacterial growth. Part A focuses on deriving an algebraic rule to link the number of bacteria at different time points, calculating the number of bacteria after a specific duration, and determining the time required for the colony to reach a certain size. Part B examines the relationship between the number of bacteria and the size of the colony, the impact of different replication rates, the implications of different colony sizes at the start, and the effects of growth-limiting factors such as environmental conditions, clay composition, oxygen levels, and nutrient availability. The assignment references several journal articles and books to support the analysis and findings.

Algebra investigation

Table of Contents
Part A.........................................................................................................................................................3
1. Write down an algebraic rule linking the number of bacteria present at a particular time to the
number present one minute previously....................................................................................................3
2. Write down an expression for the number of bacteria present after t minutes.....................................3
3. Calculate the number of bacteria present after 2 hours........................................................................3
Part B.........................................................................................................................................................3
a. The relationship between the number of bacteria and the size of the colony.......................................3
b. Different rates of replication................................................................................................................4
c. Colonies of different sizes at the start..................................................................................................4
d. Effect of growth limiting factors..........................................................................................................5
REFERENCES..........................................................................................................................................6

Part A
1. Write down an algebraic rule linking the number of bacteria present at a particular time to the
number present one minute previously.
The algebra rule which can be used for linking the number of bacteria present at a particular time to the
number present one minute previously is as following:
It can be solve using an exponential equation
a(r)^n
A is constant which is 0, N is number of bacteria and There is a recurrence relation.
2. Write down an expression for the number of bacteria 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. Calculate the number of bacteria present after 2 hours
a(2 hours =120 minutes) = 2(2) ^121
a(120)= 2(2) ^121 = 5.316911983139663e+36
4.Calculate the time for the colony to reach 1 million bacteria
18 minutes 30 seconds
Part B
a. The relationship between the number of bacteria and the size of the colony
Bacteria grow on solid media as colonies, a colony is described as visible mass of micro-
organism all originating from an individual mother cell. Hence, a colony constitutes a clone of

bacteria all inherently alike (Andrade-Olivei and et.al., 2015). The size of colony can vary from
large colonies to tiny colonies less than 1mm = punctiform(pin-point). Measure with a millimetre
rule. In the identification of bacteria and fungi much weight is placed on the way organism
grows on or in media (Khudoyberdiyev, Ladra and Omirov).
20. This activity will assist in identifying the cultural characteristics of a bacterium ion an agar
plate known as colony morphology. However, it is not necessary to see the importance of
colonial morphology at first. It can be essential when identifying the bacterium. Characteristics
of the colonies may help to pinpoint the identify od the bacterium. Various species of bacteria
can produce very different colonies.
b. Different rates of replication
On the basis of growth conditions, bacteria may divide slowly or rapidly, in rich media the
number of cells can double in every 18 minutes. On the other hand, nutrients are scare, the doubling time
can be as long as 180 minutes. The bacterial cells accomplish this by differentiating the rate of re-
initiation of replication. Re-initiation has to occur at the same frequency as the cell doubling time
(Rasouli and Davvaz, 2015).
c. Colonies of different sizes at the start
Colony morphology is a technique used in order to define the characteristics of individual colony
of bacteria growing 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 being
transferred eventually in the first case to oxygen and in the second 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).