Recall that y varies inversely with x if and only if exist a constant k such that:
[tex]y=\frac{k}{x}\text{.}[/tex]Since g(n) varies inversely with n, we can set the following equation:
[tex]g(n)=\frac{k}{n}\text{.}[/tex]Now, we know that g(n)=13 when n=2, then:
[tex]13=\frac{k}{2}\text{.}[/tex]Multiplying the above equation by 2 we get:
[tex]\begin{gathered} 13\times2=\frac{k}{2}\times2, \\ 26=k\text{.} \end{gathered}[/tex]Therefore:
[tex]g(n)=\frac{26}{n}\text{.}[/tex]Setting g(n)=4 we get:
[tex]4=\frac{26}{n}\text{.}[/tex]Multiplying the above equation by n we get:
[tex]\begin{gathered} 4\times n=\frac{26}{n}\times n, \\ 4n=26. \end{gathered}[/tex]Dividing the above equation by 4 we get:
[tex]\begin{gathered} \frac{4n}{4}=\frac{26}{4}, \\ n=6.5. \end{gathered}[/tex]Answer: n=6.5.
