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