Answer
$
f(x)=16,384\left(\frac{1}{4}\right)^x
$
Work Step by Step
Use the ratio method to see if the data can be expressed as an exponential function. We see that
$$
\frac{f(2)}{f(1)}=\frac{f(5)}{f(4)}=\frac{f(9)}{f(8)}=\frac{1}{4}
$$ This means that $b= 1/4$.
Using $f(1)=4096$ we find $4096=a b=a\left(\frac{1}{4}\right)$, so $a=16,384$.
Hence $$
f(x)=16384\left(\frac{1}{4}\right)^x
$$
