the exponential function is of the form
[tex]g(x)=a(b)^x[/tex]
In this problem
For x=0, g(x)=4
that means
the initial value a is equal 4
a=4
substitute
[tex]g(x)=4(b)^x[/tex]
For x=1, g(x)=12
substitute in the expression above
[tex]\begin{gathered} 12=4(b)^1 \\ 4b=12 \\ b=\frac{12}{4} \\ b=3 \end{gathered}[/tex]
therefore
[tex]g(x)=4(3)^x[/tex]
the answer is the third option
