Homework question I don't understand

I've been given this homework problem that involves finding the range of the initial value for the number of the population infected in a week for some disease spread. I don't quite understand how to go about answering the question and translating it in code. Attached is the homework problem pdf and below is what I came up with so far (I know this code doesn't work)

for n=1:100
  R=(x(n+1)^2)/x(n)-((x(n))^2);
  (0<x(1))&&(x(1)<1);

    x(n+1)=R*x(n)*(1-x(n));
end
plot(x)

Answer 1

[Daniel Vasilaky]

Look at the plot for various x and R. Remember that R=4.6692016091 is a critical point. For example, if say x=.02 and R=4<4.6692016091 , we get unstable plot. For R=1 we smoothly converge to 0. Here is the code for x=.02 and R=4.

x=.02; % initialize x

for i=1:100, %loop say 100 times

x=4*(x-x^2); % Set R=4,this is the recurrence x_i+1=4*(x_i - x_i^2)

t(i,1)=i;% store i in the first column of 100-by-2 matrix

t(i,2)=x;% store x in the second column

end;

plot(t(:,1),t(:,2)); % plot the 1st column vs. 2nd column.

It's a start, hope it helps.

[Celeste Knight]

how exactly did you find R in the first place? and when i try to edit my code to what you have posted i just get an error