Wikipedia:Reference desk/Archives/Mathematics/2012 February 8

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February 8

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Problem solving : work backward

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How do I solve the problem? In June 2005, a sixth grade class planted a tree in the schoolyard. The tree grew about 3 inched a year. If the tree was 38 inches high in June 2010, about how high was the tree when it was planted? — Preceding unsigned comment added by 67.8.185.89 (talk) 04:16, 8 February 2012 (UTC)[reply]

Start with:
PRESENT HEIGHT = INITIAL HEIGHT + GROWTH
Now subtract GROWTH from both sides:
PRESENT HEIGHT - GROWTH = INITIAL HEIGHT + GROWTH - GROWTH
PRESENT HEIGHT - GROWTH = INITIAL HEIGHT
Now expand GROWTH:
PRESENT HEIGHT - (YEARS OF GROWTH)×(GROWTH PER YEAR) = INITIAL HEIGHT
Now just plug in your values to get the answer. StuRat (talk) 04:50, 8 February 2012 (UTC)[reply]

Time lag in second-order positive feedback

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In a second-order positive feedback loop that would produce hyperbolic growth with no time lag, what's the shape of the curve if there's a constant time lag? And what about a time lag that's inversely proportional to the quantity -- does the latter still produce a singularity? NeonMerlin 04:46, 8 February 2012 (UTC)[reply]

I don't have an exact solution, but the double exponential function   comes close to solving  . As for the shrinking delay,   (where   solves  ) solves  . --Tardis (talk) 06:32, 16 February 2012 (UTC)[reply]

Value of infinite limit

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I'm having trouble with this, the equation of motion from the free fall article (position as a function of time) for a body falling under gravity but subject to air resistance proportional to the square of velocity:

 

As t becomes infinite, the equation should become

 

but I get a -ln2 term appearing. What's wrong?86.174.199.35 (talk) 17:19, 8 February 2012 (UTC)[reply]

It doesn't start going at rerminal velocity immediately so you need y0 adjusted by some constant amount. Dmcq (talk) 17:45, 8 February 2012 (UTC)[reply]
Of course. 86.174.199.35 (talk) 08:28, 9 February 2012 (UTC)[reply]
Actually thinking about it one can have an amount that grew to infinity if it did it slowly enough but that's not what's happening in this case thankfully :) Dmcq (talk) 13:06, 9 February 2012 (UTC)[reply]