Bacteria and Algebra.

Part A

For one strain of bacteria, each bacterium divides into two every minute.

The table shows the number of bacteria present in a particular sample for the first 5 minutes.

Time (minutes) number of bacteria present

0 2

1 4

2 8

3 16

4 32

5 64

Write down an algebraic rule linking the number of bacteria present at a particular time to the number present one minute previously.

= y2t+2*y2t

Write down an expression for the number of bacteria present after t minutes

The solution: 22t, where t stands for time in minutes.

Calculate the number of bacteria present after 2 hours. (State any assumptions you make.)

Given that t is time in minutes, then 2 hours is equivalent to 120 minutes. Therefore the solution is: 22*120=1.76684706477838E723

Calculate the time for the colony to reach 1 million bacteria.

Given that the time taken is t and the initial bacteria are 2, then we have:

22t=1000000,

4t=1000000,

tlog4=log 1000000

t=9.96578428466209 minutes

We therefore say that it takes approximately 10 minutes to have bacteria colony reach 1 million.

Part B

Use algebra to extend this model for the growth of bacteria colonies.

You could investigate:

The relationship between the number of bacteria and the size of the colony

Different rates of replication

Colonies of different sizes at the start

Effect of growth limiting factors (such as build-up of waste products, competition for space)

Explain all the steps of your analysis and state any assumptions you make in construct…

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