The Fibonacci sequence is a model for rabbit population growth. It starts with t

Question

The Fibonacci sequence is a model for rabbit population growth. It starts with two 1's then the next number is the sum of the prior two numbers nk=nk?1 +nk?2 . The first few

numbers are: 1 1 2 3 5 8 13 . As the sequence gets large the ratio of one number over the prior number approaches a constant called the Golden Ratio nk? ? . Write a function

to compute the Golden Ratio using the Fibonacci sequence. Compare each new value to the last value of the Golden Ratio then exit if the difference is less than 2*eps. Limit the total number of iterations to 200. Plot on the same graph both the approximation of the Golden Ratio and the Fibonacci number for each k on separate y axises.

Explanation / Answer

x1=1;
x2=1;
GRatio=x2/x1;

for i=1:200
t=x1+x2;
GRatioTemp=t/x2;
if((GRatio-GRatioTemp)<(2*eps))&&((GRatioTemp-GRatio)<(2*eps))
break
end
Table(i,1)=x2;
Table(i,2)=GRatio;
GRatio=GRatioTemp;
x1=x2;
x2=t;
  
end


GRatio

plot(Table(:,2))
plot(Table(:,1))
  

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