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47 training minutes?

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187726.18 in reply to 187726.16
Date: 6/25/2011 9:26:07 AM
Overall Posts Rated:
147147
N^c (where c is a constant) is polynomial..
c^N is exponential..

a simple equation:
c^48 = 100 /log
48logc = log100
c~1.1007

now for c=1.1 we have:
1.1007^48 ~100
1.1007^47 ~ 90.87

however, the constant can have whatever value, and then they can scale it to 100%..
for example, if c were 1.15, then:
1.15^48 = 819.4
1.15^47 = 712.52

and 712.52/819.3 ~ 87%..



Beautiful math. So 47 minutes should get you between 87-95% of full training.

And if the model is exponential - which is impossible to know for sure - then anything less than 48+ minutes is pretty damaging.

By your model, 40 minutes only gives you 46% of full training.

This Post:
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187726.19 in reply to 187726.18
Date: 6/25/2011 9:32:47 AM
Overall Posts Rated:
959959
but it could be also more slightly choosing an small N like 1.0001, or making the difference smaller through an constant affecting t.

c_1^(t*c_2) && c_2 <1
but you could make it also worse with the same tricks, in a different direction.

This Post:
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187726.20 in reply to 187726.19
Date: 6/25/2011 9:45:33 AM
Overall Posts Rated:
147147
You're right, without knowing the constant this is all worthless conjecture.

However, Fenris' equation is the most mathematically efficient. His equation penalizes pretty harshly for not meeting the full 48 minutes, though, so maybe the constant is lower?

As I said at the beginning, worthless conjecture.........

This Post:
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187726.21 in reply to 187726.20
Date: 6/25/2011 10:28:43 AM
Overall Posts Rated:
104104
I feel stupid. :(
Is this related to Algebra cause I just took it. Oh well, maybe I should've paid more attention. :)

This Post:
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187726.22 in reply to 187726.21
Date: 6/25/2011 4:05:08 PM
Overall Posts Rated:
406406
My crystal ball says the numbers guessed in this thread are probably correct.