# Bacterial growth Lab report

Bacterialgrowth

Labreport

1. 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 8th hour Number at the 10th hour Number at the 12th hour Number at the 24th 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:

An= a(r)n-1 where

An=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

1. Bacteria with the highest growth rate are those in strain 4

2. Bacteria with the lowest growth rate are those in strain 5

3. 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.

4. Bacteria are known to double or grow in a geometric manner hence the model here is realistic.

Fromthe model An= a(r)n-1 , the number of bacteria at different hours n will be calculated inrelation to the initial number a that was used in starting theculture.

Inthe 8thhour, 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 10thhour, 12thand 24thhour, the working is done in the same way replacing the values of aand r appropriately. The numbers calculated are given in the tableabove.

1. 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 , 316-333.