We have a function:
[tex]f(x)=b^x[/tex]
We know one point of the function, that is (2, 9/16).
Then, we can replace f(x) with 9/16 and x with 2 and calculate b:
[tex]\begin{gathered} f(x)=b^x \\ f(2)=\frac{9}{16} \\ b^2=\frac{9}{16} \\ b=\sqrt[]{\frac{9}{16}} \\ b=\frac{3}{4} \end{gathered}[/tex]
Then, the correct function is:
[tex]f(x)=(\frac{3}{4})^x[/tex]
Answer: f(x) = (3/4)^x
