[tex]\begin{gathered} y=-0.32x^2+36.25x+5846.18 \\ A) \\ Vertex(\frac{-b}{2a},y(\frac{-b}{2a})) \\ a=-0.32 \\ b=36.25 \\ \frac{-b}{2a}=\frac{-(36.25)}{2(-0.32)}=\frac{-36.25}{-0.64}=56.641 \\ y=-0.32(56.641)^2+36.25(56.641)+5846.18 \\ y=6872.791 \\ Vertex(56.64,6872.79) \\ \\ B) \\ \\ The\text{ population will be maximized at 6872.79 in the year 2046.64} \\ \\ C) \\ 1995-1990=5 \\ Hence \\ 56.64-5=51.64 \\ For\text{ 51.64 years the population will increase} \end{gathered}[/tex]
