If g is an exponential function, it has the form:
[tex]g(x)=a\cdot b^x[/tex]We know two values of the function, and we will use them to find a and b.
We start by finding b, as we have:
[tex]\begin{gathered} \frac{g(3)}{g(2)}=\frac{ab^3}{ab^2}=b^{3-2}=b \\ b=\frac{g(3)}{g(2)}=\frac{33.603}{33.5359}\approx1.0002 \end{gathered}[/tex]Then, we use one of the points to find a:
[tex]\begin{gathered} g(3)=a\cdot1.0002^3=33.603 \\ a=\frac{33.603}{1.0002^3}\approx\frac{33.603}{1.0006}\approx33.583 \end{gathered}[/tex]We can then write g(x) as:
[tex]g(x)=33.583\cdot1.0002^x[/tex]