Question 1025991
{{{ f(x) = -2x^2 + 30x + 17 }}}
( Is this correct? )
The formula for maximum is:
{{{ x[max] = -b/(2a) }}}
{{{ x[max] = -30/( 2*(-2) ) }}}
{{{ x[max] = 15/2 }}}
Plug this result back into formula
{{{ f( 15/2 ) = -2*( 15/2 )^2 + 30*( 15/2 ) + 17 }}}
{{{ f( 15/2 ) = -225/2 + 225 + 17 }}}
{{{ f( 15/2 ) = 225/2 + 17 }}}
{{{ f( 15/2 ) = 112.5 + 17 }}}
{{{ f( 15/2 ) = 129.5 }}}
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(a)
The maximum population was 129,500
(b)
1993 + 15/2 = 1993 + 7.5
1993 + 7.5 = 2000
The maximum was reached in 2000
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Here's the plot:
{{{ graph( 400, 400, -2, 20, -15, 150, -2x^2 + 30x + 17 ) }}}