Answer
$f(x)=(\frac{1}{6})^x$
Work Step by Step
First, we have to find the function, by calculating the value of the base, $a\\$.
If the function contains this point (-2,36), then $f(-2)=36\\$.
This means: $a^{-2}=36\\$.
By the law of exponents: $a^{-x}=(\frac{1}{a})^x$
Thus, the equation above is equivalent to: $(\frac{1}{a})^{2}=36\\$
We take the square root of both sides but take only the positive root since $a \gt0$:
$\frac{1}{a}=\sqrt{36}
\\\frac{1}{a}=6\\$
$a \cdot \frac{1}{a} = 6 \cdot a \\$
$1=6a \\$
$\frac{1}{6}=a$
Therefore, with $a=\frac{1}{6}$, the function is: $f(x)=(\frac{1}{6})^x$.
