Question 982510
Let {{{ n }}} = the number of fruits at start
{{{ n }}} doubles every minute for {{{ 60 }}} min
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start: {{{ n }}}
1 min: {{{ 2n }}}
2 min: {{{ 4n }}}
3 min: {{{ 8n }}}
. . . . . . . . . . . .
60 min: {{{ ( 2^60 )*n }}}
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Let {{{ k }}} = time in min when basket
is 1/8 full
Find:
{{{ (1/8)*( 2^60 )*n = ( 2^k )*n }}}
{{{ 2^k = ( 1/8 )*2^60 }}}
{{{ ( 2*k )*( 2^3 ) = 2^( 60 ) }}}
{{{ 2^( k + 3 ) = 2^( 60 ) }}}
{{{ k + 3 = 60 }}} 
{{{ k = 57 }}}
After 57 min the basket was 1/8 full
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check:
Suppose {{{ n = 1 }}}
I want to show:
{{{ 2^57 = (1/8)*2^60 }}}
{{{ 2^( 60-57) = 8 }}}
{{{ 2^3 = 8 }}}
{{{ 8 = 8 }}}
OK