Algebra Investigation

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