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patdistheman
 3 years ago
(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?
patdistheman
 3 years ago
(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?

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LogicalApple
 3 years ago
Best ResponseYou've already chosen the best response.1Can this be a two part function? Or does it have to be one function?

patdistheman
 3 years ago
Best ResponseYou've already chosen the best response.0I do not understand what that means.

patdistheman
 3 years ago
Best ResponseYou've already chosen the best response.0As far as I am concerned anything that will generate the answer.

LogicalApple
 3 years ago
Best ResponseYou've already chosen the best response.1If 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?

patdistheman
 3 years ago
Best ResponseYou've already chosen the best response.0The floor function generates a rounded down number?

LogicalApple
 3 years ago
Best ResponseYou've already chosen the best response.1Yes, it basically truncates (gets rid of) the decimal.

patdistheman
 3 years ago
Best ResponseYou've already chosen the best response.0I am attempting to determine if lets say there were 1072 cycles... what would b equal?

LogicalApple
 3 years ago
Best ResponseYou've already chosen the best response.1I see what you are saying. Hm.

patdistheman
 3 years ago
Best ResponseYou've already chosen the best response.0I 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.

LogicalApple
 3 years ago
Best ResponseYou've already chosen the best response.1I can think of a recursive formula...

patdistheman
 3 years ago
Best ResponseYou've already chosen the best response.0I would greatly appreciate that if you could show me how you generated it.

LogicalApple
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1356826201787:dw

LogicalApple
 3 years ago
Best ResponseYou've already chosen the best response.1Since the result of each cycle is the input into the next one, the function can be defined recursively.

patdistheman
 3 years ago
Best ResponseYou've already chosen the best response.0I am not certain how to compute that formula.

LogicalApple
 3 years ago
Best ResponseYou've already chosen the best response.1That 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.

patdistheman
 3 years ago
Best ResponseYou've already chosen the best response.0Is there a way to put that formula into a spreadsheet?

LogicalApple
 3 years ago
Best ResponseYou've already chosen the best response.1dw: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.

LogicalApple
 3 years ago
Best ResponseYou've already chosen the best response.1Here Ba is the (rounded off) value of B on the ath cycle. So, B_10 would give you the result of the 10th cycle.

patdistheman
 3 years ago
Best ResponseYou've already chosen the best response.0I 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.

LogicalApple
 3 years ago
Best ResponseYou've already chosen the best response.1Let'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.
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