Graphing parametric equations

Question

I am very unsure as to how to graph $y = \exp(t)$, $z = \exp(t)\cos(t)$ and $x = \exp(t)\sin(t)$.

Initially, I thought the traces were circles parallel to the $xz$-plane and increased across the positive $y$-axis (where $y > 0$) in a spiral-like manner. Upon graphing it on matlab, it showed a single curve and now I'm confused as to where I may have went wrong or is it due to the limitations of matlab?

Answer 1

HINT

\begin{align*} z^{2} + x^{2} = \exp(2t)\cos^{2}(t) + \exp(2t)\sin^{2}(t) = \exp(2t) = y^{2} \end{align*}