Answer:
[tex]f(x)=9^{x-1}[/tex]
Step-by-step explanation:
The general form of the exponential function is,
[tex]y=ab^x[/tex]
The points on the graph will be,
[tex](2,9),(3,27),(4,81)[/tex]
Putting the points in the function,
[tex]9=ab^2[/tex] -----------------------------------1
[tex]27=ab^3[/tex] ---------------------------------2
Dividing equation 2 by equation 1,
[tex]\Rightarrow \dfrac{27}{3}=\dfrac{ab^3}{ab^2}[/tex]
[tex]\Rightarrow 9=\dfrac{b^3}{b^2}[/tex]
[tex]\Rightarrow b=9[/tex]
Putting the value of b in equation 1,
[tex]\Rightarrow a(9)^2=9[/tex]
[tex]\Rightarrow a=\dfrac{9}{9^2}[/tex]
[tex]\Rightarrow a=\dfrac{1}{9}[/tex]
Putting all the values,
[tex]\Rightarrow y=\dfrac{1}{9}\cdot 9^x[/tex]
[tex]\Rightarrow y=9^{x-1}[/tex]
