Question 696834
Just to get a handle on this, i'll start
by saying 
{{{ W[n] = a / (2^n) }}}
where {{{ W[n] }}} is the distance traveled for week number {{{ n }}}
I'll say that {{{ n }}} starts at {{{ 0 }}}, and 
adds 1 more for each week, {{{ W }}}
{{{ W[0] = a / ( 2^0 ) }}}
{{{ W[1] = a / ( 2^1 ) }}}
{{{ W[2] = a / ( 2^3 ) }}}
etc.
Notice that for any particulart week, {{{ W[n] }}}
The value is half that of the previous week
Now let {{{ a = 4096 }}}
I want the condition:
{{{ W[n] = 4096 / ( 2^n ) }}}
{{{ 4 = 4096 / ( 2^n ) }}}
{{{ 2^n = 4096 / 4 }}}
{{{ 2^n = 1024 }}}
You can use a calculator depending on what
functions it has. At the most basic, you can take 
log base 10 of both sides
{{{ log( 2^n ) = log( 1024 ) }}}
{{{ n = log( 1024 ) / log(2) }}}
{{{ n = 3.0103 / .30103 }}}
{{{ n = 10 }}}
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Notice that I said that week one started with {{{ n = 0 }}}
so, I must add {{{ 1 }}} to each week number, so
in week number 11, the tortoise travels 4 m