Question 1036687
What you did is the right start. I think they want
you to find {{{ k }}} ( which you did ), then 
resolve the equation and find the new multiplier
with {{{ k }}} for cooling to 109 degrees F
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I'll check what you did first:
{{{ 150 = 68 + 257*e^(-25k) }}}
{{{ 82 = 256*e^( -25k ) }}}
{{{ .3203125 = e^(-25k) }}}
{{{ ln( .3203125 ) = -25k }}}
{{{ -1.13846 = -25k }}}
{{{ k = .045538 }}}
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Let the multiplier of {{{ k }}} = {{{x}}}
Now solve this equation:
{{{ 109 = 68 + 257*e^(-x*k) }}}
{{{ 41 = 257*e^(-x*k) }}}
{{{ .159533 = e^(-x*k) }}}
{{{ ln( .159533 ) = -x*k }}}
{{{ -1.8355 = -x*.045538 }}}
{{{ x = 40.3071 }}}
and
{{{ .3071*60 = 18.426 }}}
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It takes about 40 min and 18 sec for 
the cake to cool to 109 degrees F
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Check my math, and you may want a
2nd opinion, too