Hello!
[tex]\large\boxed{y = 5(\frac{1}{2})^{x} }[/tex]
Recall that the equation of an exponential graph is:
[tex]y = a(b)^{x}[/tex]
We can see from the graph there is a y-intercept at y = 5. Plugging in 0 for x results in:
[tex]5 = a(b)^{0}\\\\5 = a(1)\\\\a = 5[/tex]
Solve for b by plugging in another point on the graph:
[tex]10 = 5(b)^{-1}\\\\2 = b^{-1}\\\\b = 1/2[/tex]
Write the final equation:
[tex]y = 5(\frac{1}{2})^{x}[/tex]
