Suppose that a certain type of bacteria divides (into two) in a given time perio

Question

Suppose that a certain type of bacteria divides (into two) in a given time period with a probability of 75%, and that if it does not divide, it dies. The rand function is useful for simulations of probability because it returns a random number between 0 and 1. Therefore, you could simulate the likelihood of a bacterium dividing by checking if the rand function returns a number less than 0.75 (and if so, the bacterium divides and lives!) You want to simulate a number of generations of bacterial growth. Starting with one bacterium, suppose that it divides into two with probability p = 0.75, and if it does not divide, it dies. In the next generation, the offspring will also divide or die (independently) with a probability of p = 0.75. If no bacteria survive, the colony becomes extinct. To get a good idea of the population, you will need to run this simulation many times. The best way to approach this problem (and many like it) is to start small. (I like to think of this as

Explanation / Answer

close all,

clear all,

clc,

SurvivalProb = 0.75;

%%%%%% Single Bacteria Lives or Dies %%%%%%%%%%%%%

No_of_Simulations = 10;

Initial_No_of_Bacteria=10;

BacteriaGrowth=[];

for i=1:No_of_Simulations

BacteriaGrowth(i) = Initial_No_of_Bacteria;

No_of_Bacteria = Initial_No_of_Bacteria;

for j=1:No_of_Bacteria

tempProb = rand;

if (tempProb >= SurvivalProb),

BacteriaGrowth(i) = BacteriaGrowth(i)+2; % Bacteria diviedes and increment by 2.

No_of_Bacteria = No_of_Bacteria+1;

else

BacteriaGrowth(i) = BacteriaGrowth(i)-1; % bacteria Dies and decrement by 1.

No_of_Bacteria = No_of_Bacteria-1;

end

end

end

figure,

plot(BacteriaGrowth); title('Bacterial Growth Vs. Simultion'); xlabel('---- Simul;ation No. ---->'); ylabel('---- No. of Bacteria --->');

%%%%%% Genetical Growth %%%%%%%%%%%%%

Initial_No_of_Bacteria=1000;

No_of_Bacteria=Initial_No_of_Bacteria;

Generation = [];

TotalBacteria=[];

for i=1:3

Generation(i)=0;

TotalBacteria(i)=0;

end

Generation(1) = Initial_No_of_Bacteria;

TotalBacteria(1) = Initial_No_of_Bacteria;

%%%%%%%%%%%%% Generation-1 %%%%%%%%%%%

BacteriaGrowth(1) = Initial_No_of_Bacteria;

No_of_Bacteria = Initial_No_of_Bacteria;

tempGen=0;

tempDie=0;

for j=1:No_of_Bacteria

tempProb = rand;

if (tempProb >= SurvivalProb),

No_of_Bacteria = No_of_Bacteria+2;

tempGen=tempGen+2;

else

No_of_Bacteria = No_of_Bacteria-1;

tempDie=tempDie+1;

end

end

Generation(2) = tempGen;

TotalBacteria(2) = No_of_Bacteria;

%%%%%%%%%%%%% Generation-1 %%%%%%%%%%%

%%%%%%%%%%%%% Generation-2 %%%%%%%%%%%

BacteriaGrowth(3) = TotalBacteria(2);

No_of_Bacteria = TotalBacteria(2);

tempGen=0;

tempDie=0;

for j=1:No_of_Bacteria

tempProb = rand;

if (tempProb >= SurvivalProb),

No_of_Bacteria = No_of_Bacteria+2;

tempGen=tempGen+2;

else

No_of_Bacteria = No_of_Bacteria-1;

tempDie=tempDie+1;

end

end

Generation(3) = tempGen;

TotalBacteria(3) = No_of_Bacteria;

%%%%%%%%%%%%% Generation-2 %%%%%%%%%%%

figure,

plot(Generation); title('------------- Bacteria Growth Vs Generation No. ---->'); xlabel('---- Generation No. ---->'); ylabel('----- No. of Bacteria ---->');

plot(TotalBacteria); title('------------- Total No. of Bacteria Vs Generation No. ---->'); xlabel('---- Generation No. ---->'); ylabel('----- No. of Bacteria ---->');

Generation

TotalBacteria

%%%%%% No. of Bacteria in each generations %%%%%%%%%%%%%

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