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