y = \\frac{1}{8}e^{x}\ny = \\frac{1}{2}e^{x}\ny = 2e^{x}\ny = 8e^{x}

Explanation:

Step1: Recall the general form of exponential - function

The general form of an exponential function is $y = ae^{x}$, and when $x = 0$, $y=a$.

Step2: Find the y - intercept of the graph

From the graph, when $x = 0$, $y = \frac{1}{2}$.

Step3: Determine the value of 'a'

Substituting $x = 0$ and $y=\frac{1}{2}$ into $y = ae^{x}$, we get $\frac{1}{2}=a\times e^{0}$. Since $e^{0}=1$, then $a=\frac{1}{2}$. So the function is $y=\frac{1}{2}e^{x}$.

Answer:

$y=\frac{1}{2}e^{x}$