A particle moves in the $$xy$$-plane so that its position for $$t \geq 0$$ is given by the parametric equations $$x = \ln(t + 1)$$ and $$y = kt^2$$, where $$k$$ is a positive constant. The line tangent to the particle’s path at the point where $$t = 3$$ has slope $$8$$. What is the value of $$k$$?