o $y = \\frac{1}{8}e^{x}$\no $y = \\frac{1}{2}e^{x}$\no $y = 2e^{x}$\no $y = 8e^{x}$
o $y = \\frac{1}{8}e^{x}$\no $y = \\frac{1}{2}e^{x}$\no $y = 2e^{x}$\no $y = 8e^{x}$
Answer
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 given graph
The graph intersects the y - axis at the point $(0, \frac{1}{2})$. When $x = 0$, substituting into $y=ae^{x}$, we get $y=a\times e^{0}=a$. Since $e^{0}=1$, when $x = 0$, $y=a$.
Step3: Determine the value of a
Since the y - intercept of the graph is $\frac{1}{2}$, then $a=\frac{1}{2}$. So the function of the graph is $y=\frac{1}{2}e^{x}$.
Answer:
$y=\frac{1}{2}e^{x}$