Step 1 :The doubling time for an exponential function is given by the formula T = ln(2)/ln(b), where b is the base of the exponential function.
Step 2 :In this case, b = 1.2.
Step 3 :So, we need to calculate T = ln(2)/ln(1.2).
Step 4 :Using the formula, we get T = 3.8017840169239308.
Step 5 :So, the doubling time for the function \(f(x)=9(1.2)^{x}\) is approximately \(\boxed{3.802}\).