[tex]y = \frac{1}{2} e^{x}[/tex] equation is represented by the given graph.
What is graph?
"Graph is defined as the representation of relation between two variables on the coordinate plane."
According to the question,
From the observation of the graph,
for x= 0
y- intercept = [tex]\frac{1}{2}[/tex]
a. [tex]y = \frac{1}{8} e^{x}[/tex]
Substitute x = 0 in the equation we get,
[tex]y = \frac{1}{8} e^{0}[/tex]
⇒ [tex]y = \frac{1}{8}[/tex]
Therefore,
Option (a) is not the correct answer.
b. [tex]y = \frac{1}{2} e^{x}[/tex]
Substitute x = 0 in the equation we get,
[tex]y = \frac{1}{2} e^{0}[/tex]
⇒ [tex]y = \frac{1}{2}[/tex]
which is same as graph value.
Hence, Option (b) is the correct answer.
Learn more about graph here
https://brainly.com/question/10712002
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