Answer:
[tex]y = 3(\frac{1}{3} )^{x}[/tex]
Step-by-step explanation:
See the attached graph.
The points (0,3) and (1,1) are on the graph of the exponential function.
Let the function be [tex]y = a(b)^{x}[/tex] ....... (1)
Now, satisfying the point (0,3) we get from the equation (1),
[tex]3 = a(b)^{0} = a[/tex]
Therefore, the initial value of the function is a = 3
Hence, the equation becomes [tex]y = 3(b)^{x}[/tex] ......... (2)
Now, satisfying the point (1,1) we get from equation (2)
[tex]1 = 3 (b)^{1}[/tex]
⇒ b = 1/3
So, the final equation becomes [tex]y = 3(\frac{1}{3} )^{x}[/tex] (Answer)
