5. (15 points) Let fibbe the Fibonacci members where fibo = 0 and fiby = 1. Also, let o=11V (a) (10 points) Prove that the number of digits in the Fibonacci representation of all integers in rangefib.fiba+) is n. (b) (5 points) Write a Python program that computes the mmber of digits in the Fibonacci representation of any number and compares it to the functions log2(Start) + 2 and logo(Start) + 2. To be most useful, convert the floating point answers to integers in some useful way. If you do this, the first 11 rows of this table are shown below. Expand the table so that there are 30 numerical rows in addition to the header. Include the Python program in your PDF file. Make a conjecture about the number of digits in the Fibonacci representation of a number as a function of n and include it in your PDF file. Start End Num Digits Log2(Start) +2 LogPhi(Start)+2 2.0 2.0 2 2 3 3 .0 3.0 4.0 7 5 4.0 5.0 12 65.0 6.0 20 7 6.0 8 6.0 97.0 10 8 .0 10.0 8.0 11.0 144 232 12 9.0 12.0 - 9.0 SE 5. (15 points) Let fibbe the Fibonacci members where fibo = 0 and fiby = 1. Also, let o=11V (a) (10 points) Prove that the number of digits in the Fibonacci representation of all integers in rangefib.fiba+) is n. (b) (5 points) Write a Python program that computes the mmber of digits in the Fibonacci representation of any number and compares it to the functions log2(Start) + 2 and logo(Start) + 2. To be most useful, convert the floating point answers to integers in some useful way. If you do this, the first 11 rows of this table are shown below. Expand the table so that there are 30 numerical rows in addition to the header. Include the Python program in your PDF file. Make a conjecture about the number of digits in the Fibonacci representation of a number as a function of n and include it in your PDF file. Start End Num Digits Log2(Start) +2 LogPhi(Start)+2 2.0 2.0 2 2 3 3 .0 3.0 4.0 7 5 4.0 5.0 12 65.0 6.0 20 7 6.0 8 6.0 97.0 10 8 .0 10.0 8.0 11.0 144 232 12 9.0 12.0 - 9.0 SE