Question 1076999
As a decimal, x% = {{{ .01x }}}
Let {{{ N }}} = the number of frog to begin with
{{{ N/2 }}} = the number of frogs after {{{ 8 }}} yrs
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{{{ N/2 = N*( 1 - .01x )^8 }}}
Divide both sides by {{{ N }}}
{{{ 1/2 = ( 1 - .01x )^8 }}}
Take the eigthth root of both sides
{{{ ( 1/2 )^(1/8) = 1 - .01x }}}
{{{ .917 = 1 - .01x }}}
{{{ .01x = 1 - .917 }}}
{{{ .01x = .083 }}}
{{{ x = 8.3 }}}
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check:
{{{ 1/2 = ( 1 - .01x )^8 }}}
{{{ 1/2 = ( 1 - .083 )^8 }}}
{{{ .5 = .917^8 }}}
{{{ .5 = .49998 }}}
close enough
check the math