Question 87064
the formula is {{{ P = 0.64x^2 - 0.045x + 1 }}} 


Find the year (x) after which th epopulation is 64550 (P). Now P in the formula is in thousands --> P=64.55


So, {{{ 64.55 = 0.64x^2 - 0.045x + 1 }}}


Multiply everything by 1000 to get rid of decimals: {{{ 64550 = 640x^2 - 45x + 1000 }}}

{{{ 640x^2 - 45x + 1000 = 64550 }}} 
{{{ 640x^2 - 45x - 63550 = 0 }}} and simplify by factor of 5
{{{ 128x^2 - 9x - 12710 = 0 }}}


I don't think i want to try factorising this so straight to formula:


{{{ x = (-b +- sqrt(b^2 - 4ac) )/(2a) }}}
{{{ x = (-(-9) +- sqrt((-9)^2 - 4(128)(-12710)) )/(2(128)) }}}
{{{ x = (9 +- sqrt(81 + 6507520) )/(256) }}}
{{{ x = (9 +- sqrt(6507601) )/(256) }}}
{{{ x = (9 +- 2551 )/(256) }}}


so we have
{{{ x = (9 + 2551 )/(256) }}} or {{{ x = (9 - 2551 )/(256) }}}


but the second will give a negative answer and seeing as how we are talking about years, this makes no sense. So concentrate on the first answer:


{{{ x = (9 + 2551 )/(256) }}}
{{{ x = (2560)/(256) }}}
x = 10


So 10 years after 1997 --> 2007.


cheers
Jon.