Finding the Value of an Exponential Function

Consider the exponential function given by the equation:

$$ f(x) = a imes b^x $$

where $a$ is a constant, $b$ is a positive constant representing the base, and $x$ is the exponent. A specific function, $f(x)$, has the values:

$$ f(1) = 5 $$

and

$$ f(3) = 20 $$

Determine the value of $f(2)$. Use the properties of exponential functions to find the correct answer from the given options.