Bacterialgrowth
Labreport

The table below gives results of growth rates of 5 E. coli bacteria strains in a culture.
Bacteria sample strain 
a – initial number of bacteria in the culture 
Rate of growth/hr (r) 
Number at the 8^{th} hour 
Number at the 10^{th} hour 
Number at the 12^{th} hour 
Number at the 24^{th} hour 
1 
16 
4 
262144 
4194304 
67108864 
1.1259E+15 
2 
97 
3 
212139 
1909251 
17183259 
9.13189E+12 
3 
112 
7 
92236816 
4519603984 
2.2146E+11 
3.0653E+21 
4 
7 
9 
33480783 
2711943423 
2.19667E+11 
6.20406E+22 
5 
143 
2 
18304 
73216 
292864 
1199570944 
Total 
6.51059E+22 
Themodel formula for the growth rate of the bacteria is:
A_{n}= a(r)^{n1}_{ }where
A_{n}=total number of bacteria present at hour n
n= hour of culture
a= initial number of bacteria in the culture
r= rate of growth of the bacteria strain.
Sincethe growth of bacteria is suspected to be geometric in nature, thenthere should be a common ratio between the next number of bacteria inthe culture and the previous one. The numbers obtained satisfy thiscondition for the geometric series and the ratio found is the factorr.
Instrain 1, r = 64/16 = 256/64 = 1024/256 = 4096/1024 = 16384/4096 =65536/16384 = 4.
Instrain 2, r = 291/97 = 873/291 = 2619/873 = 7857/2619 = 23571/7857 =70713/23571 = 3
Instrain 3, r = 784/112= 5488/784 = 38,416/5488 = 268,912/38,416, = 1,882,384/268,912 =13,176,688/1,882,384 = 7
Instrain 4, r = 63/7 = 567/63 = 5103/567 = 45,927/5103= 413,343/45,927 = 3,720,087/413,343 = 9
Instrain 5, r = 143/286 = 572/286 = 1144/572 = 2288/1144 = 4576/2288 =9153/4576 = 2
Therefore

Bacteria with the highest growth rate are those in strain 4

Bacteria with the lowest growth rate are those in strain 5

The most manageable strain in the culture is strain 5 since it has the lowest growth rate amongst the five strains. They can be destroyed before their numbers reach detrimental levels.

Bacteria are known to double or grow in a geometric manner hence the model here is realistic.
Fromthe model A_{n}= a(r)^{n1}_{ }, the number of bacteria at different hours n will be calculated inrelation to the initial number a that was used in starting theculture.
Inthe 8^{th}hour, the number of bacteria in the culture will be as follows:
Strain1 A = 16*(4)^7 = 262144
Strain2 A = 97*(3)^7= 212139
Instrain 3 A =112*(7)^7= 92236816
Instrain 4 A =7*(9)^7 = 33480783
Instrain 5 A =143*(2)^7 = 18304
Assuminga geometric series in all cases, in the 10^{th}hour, 12^{th}and 24^{th}hour, the working is done in the same way replacing the values of aand r appropriately. The numbers calculated are given in the tableabove.

Other factors that should be considered when modeling the growth of bacteria such as E. coli include the genetic structure of the bacteria and culture medium. Marr in his paper also states that the rate of synthesis of amino acids and ATP’s which are essential in growth are factors that affect growth rate of bacteria strains [ CITATION Mar91 l 1033 ]. It is necessary to consider such factors in the growth models.
References
Marr, A. (1991). Growth rate of Eschereria coli. Microbiological Reviews , 316333.