Question 1068452
I'm not sure I get it, but here goes:
If the water level doubles each day and it takes 40
days to fill the pond, how long does it take to 
fill 1/4 of the pond?
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I'll start with the water level at {{{ h(0) }}} units ( any units of length )
I can say:
{{{ h(0)*2^40 }}}| is the full level.
Now I want to take {{{ 1/4 }}} of that
{{{ (1/4)*h(0)*2^40 }}} is the 1/4 full level
Now let {{{ t }}} = the number of days it takes to reach {{{ 1/4 }}} fiull
{{{ (1/4)*h(0)*2^40 = h(0)*2^t }}}
{{{ 2^40 = 4*2^t }}}
{{{ 2^40 = 2^2*2^t }}}
{{{ 2^40 = 2^( t + 2 ) }}}
{{{ 40 = t + 2 }}}
{{{ t = 38 }}}
It takes 38 days to be 1/4 filled
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{{{ 2^40 = 2^( t+2 ) }}}
Definitely get another opinion on this.
I don't know how to prove this result