Chapter 8 - Section 8.4 - Plane Curves and Parametric Equations - 8.4 Exercises - Page 617: 22

(a) See the graph. (b) $y=\frac{1}{x},~~x\gt0,~~y\gt0$

(a) $t=0$: $x=e^0=1$ $y=e^0=1$ Point: $(1,1)$ When $t→+∞$, $x→0$ and $y→+∞$. When $t→-∞$, $x→∞$ and $y→0$. So, $x\gt0$ and $y\gt0$ (b) $y=e^t$ $x=e^{-t}$ $x=\frac{1}{y}$ $y=\frac{1}{x}$