A particle is moving so that for $t0,v(t)<mn>0</mn>$ and $a(t)<mn>0</mn>$ where $v(t)$ is the velocity and $a(t)$ is the acceleration. If the positions, $x(t),$ of the particle are $x(1)=20$ and $v(1)=-4,$ which of the following could be the position at $t=3?$

$($A$)8$

$($B$)12$

$($C$)15$

$($D$)23$