Parametric Tangent Line Slope

For $t \geq 0$, a particle moves in the $xy$-plane with velocity components given by $x'(t) = \frac{1}{t+1}$ and $y'(t) = ke^{kt}$, where $k$ is a positive constant. The line tangent to the path of the particle at $t = 2$ is parallel to the line $y = 4x + 3$. What is the value of $k$?