Question 1042241
{{{ P(t) = 145*e^( -.092t ) }}}
Here's the plot:
{{{ graph( 500, 500, -10, 75, -20, 200, 145*e^(-.092x ) ) }}}
From the plot, I would guess that {{{ P = 70 }}}, after about
{{{ 8 }}} minutes after the race.
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Solving for {{{ P = 70 }}},
{{{ 70 = 145*e^( -.092t ) }}}
{{{ .48276 = e^( -.092t ) }}}
Take the natural log of both sides
{{{ -.728236 = -.092t }}}
{{{ t = 7.9156 }}}
{{{ t = 7.9 }}} ( rounded off )
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check:
{{{ 70 = 145*e^( -.092t ) }}}
{{{ 70 = 145*e^( -.092*7.9156 ) }}}
{{{ 70 = 145*e^(-.72824 ) }}}
{{{ 70 = 145*.48276 }}}
{{{ 70 = 70.0002 }}}
close enough