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patdistheman

(H + 1) / 10 = B H = 100 B = 10.1 (Only the rounded down result is applicable.) Next Cycle H = 110 B = 11.11 (11) Next Cycle H = 121 B = 12.2 (12) Next Cycle H = 132 B = 13.3 (13) In this example. Starting H = 100 and Cycles = 3 the result is B = 13.3. How do you determine a formula that allows you to pick a starting number for H and the number of cycles and generate B?

  • one year ago
  • one year ago

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  1. LogicalApple
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    Can this be a two part function? Or does it have to be one function?

    • one year ago
  2. patdistheman
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    I do not understand what that means.

    • one year ago
  3. patdistheman
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    As far as I am concerned anything that will generate the answer.

    • one year ago
  4. LogicalApple
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    If you're looking for the solutions in parentheses then you are looking for integer division. If you use the floor function then you will obtain what you are looking for. Have you seen the floor function before?

    • one year ago
  5. patdistheman
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    The floor function generates a rounded down number?

    • one year ago
  6. LogicalApple
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    Yes, it basically truncates (gets rid of) the decimal.

    • one year ago
  7. patdistheman
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    I am attempting to determine if lets say there were 1072 cycles... what would b equal?

    • one year ago
  8. LogicalApple
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    I see what you are saying. Hm.

    • one year ago
  9. patdistheman
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    I am not interested so much in the answer as to what B is as to how to go about solving this problem of generating the formula to determine any answer for B.

    • one year ago
  10. LogicalApple
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    I can think of a recursive formula...

    • one year ago
  11. patdistheman
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    I would greatly appreciate that if you could show me how you generated it.

    • one year ago
  12. LogicalApple
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    |dw:1356826201787:dw|

    • one year ago
  13. LogicalApple
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    Since the result of each cycle is the input into the next one, the function can be defined recursively.

    • one year ago
  14. patdistheman
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    I am not certain how to compute that formula.

    • one year ago
  15. LogicalApple
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    That is the problem with it -- it is recursive so there is no straightforward way to solve it. You would need to know the value of every cycle prior to the last cycle.

    • one year ago
  16. patdistheman
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    Is there a way to put that formula into a spreadsheet?

    • one year ago
  17. LogicalApple
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    |dw:1356828418136:dw| This corrected version of the recursion yields correct results. I am not sure how to insert something like this into a spreadsheet. However, a programming routine could help. Unfortunately for larger and larger cycles, more recursion results in longer processing and more memory demand.

    • one year ago
  18. LogicalApple
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    Here Ba is the (rounded off) value of B on the ath cycle. So, B_10 would give you the result of the 10th cycle.

    • one year ago
  19. patdistheman
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    I have to run but I will be back shortly. Can you show me a step by step solution for that formula? I am not certain how the mechanics of that work.

    • one year ago
  20. LogicalApple
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    Let's say you want to know the 4th cycle. B4 = [H3 + B3 + 1]/10 H3 = H2 + B2 B3 = [H2 + B2 + 1]/10 H2 = H1 + B1 B3 = [H1 + B1 + B2 + 1]/10 H1 = H0 + B0 = 100 + 10 = 110 B0 = 10 Thus H2 = 110 + 10 = 120 B1 = [H0 + B0 + 1]/10 = 11 B2 = [H1 + B1 + 1]/10 = 12 So far we have H2 and B2, so we can solve for B3 B3 = [H2 + B2 + 1]/10 = 13 And H3 = H2 + B2 = 120 + 12 = 132 So for B4... B4 = [H3 + B3 + 1]/10 B4 = [(132 + 13)/10] = 14 It's a lengthy process and a computer program would be advised to calculate any further values this way.

    • one year ago
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