This can be solved using a geometric sequence.
First term [tex]u_1=4[/tex] also, [tex]u_{n+1}=u_n+0.09u_n=1.09u_n[/tex].
Let x be the number of months, then the total number of hours can be computed like this:
[tex]f(x)=4\dfrac{1-1.09^x}{1-1.09}\\=44.4(1-1.09^x)[/tex]