Chapter 13 - Vector Functions - 13.1 Vector Functions and Space Curves - 13.1 Exercises - Page 894: 29

$y=e^{x/2}\\ z=e^x\\z=y^2$

Given: $x=2t; y=e^t; z=e^{2t}$ Consider $y=e^{(t)}=e^{(2t/2)}=e^{\frac{x}{2}}$ Now, next we have $z=e^{2t}\implies z=e^x$ Also, $z=e^{2t} $ This yields: $ z=(e^{(t)})^2=y^2$ Therefore, $y=e^{x/2}\\ z=e^x\\z=y^2$