Chapter 10 - Parametric Equations and Polar Coordinates - 10.1 Exercises - Page 665: 15

a) $y=\frac{lnx}{2}+1$ Domain: $x\gt 0$ b) As $t$ increases, $x$ increases.

a) Given: $x=e^{2t}$ Isolate the t: $\frac{lnx}{2}=t$ Replace t in the second equation: $y=t+1$ $y=\frac{lnx}{2}+1$ Domain: $x\gt 0$ Range: All Real Numbers b) We know that, $y=\frac{lnx}{2}+1$ $x\gt 0$ Note that $x=e^{2t}$ As $e^{2t}$ increases, $x$ increases. Therefore, as $t$ increases, $x$ increases.