The general expression for an exponential function is the following:
[tex]y=ab^x[/tex]
where b represents the base of the function.
In this case, notice that the graph of the function passes through the points (0,1) and (1,1/3), then, with these points we can find the values of a and b:
[tex]\begin{gathered} (0,1): \\ 1=ab⁰\Rightarrow a=1 \\ (1,\frac{1}{3}): \\ \frac{1}{3}=b¹\Rightarrow b=\frac{1}{3} \end{gathered}[/tex]
therefore, we have that:
the initial value is a = 1
the base is b = 1/3
the domain of the function is all real numbers.
