Question 1030293
{{{ P(t) = 2t^2 + 80t + 4000 }}}
{{{ t = 0 }}}
{{{ P(0) = 2*0^2 + 80*0 + 4000 }}}
{{{ P(0) = 4000 }}}
{{{ 2*4000 = 8000 }}}
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When does the population = {{{ 8000 }}} ?
{{{ P(t) = 8000 }}}
{{{ 8000 = 2t^2 + 80t + 4000 }}}
{{{ 2t^2 + 80t = 4000 }}}
{{{ t^2 + 40t = 2000 }}}
Complete the square
{{{ t^2 + 40t + ( 40/2 )^2 = 2000 + ( 40/2 )^2 }}}
{{{ t^2 + 40t + 400 = 2000 + 400 }}}
{{{ ( t + 20 )^2 = 2400 }}}
{{{ t + 20 = 10*sqrt(24) }}}
{{{ t = 10*4.899 - 20 }}}
{{{ t = 48.99 - 20 }}}
{{{ t = 29 }}}
Population will be double in 2029
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check:
{{{ 8000 = 2t^2 + 80t + 4000 }}}
{{{ 8000 = 2*29^2 + 80*29 + 4000 }}}
{{{ 8000 = 1682 + 2320 + 4000 }}}
{{{ 4000 = 4002 }}}
Error due to rounding off?
I think so