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