Question

If g(n) varies inversely with n and g(n)= 12 when n=2 then find the value of n when g(n)= 3 Round final answer to the tenths place. If answer is a whole number then put a zero in the tenths place before entering your answer.

Answer 1

An inverse function has this form:

$\begin{gathered} y=\frac{k}{x},\text{ where k is a constant of variation.} \\ In\text{ this case is:} \\ g(n)=\frac{k}{n} \end{gathered}$

We know that g(n) =12 when n=2, so g(2) = 12. Then

$\begin{gathered} g(2)=\frac{k}{2}\text{ = 12} \\ k=12\cdot2 \\ k=24 \end{gathered}$

So the general expression is

$g(n)=\frac{24}{n}$

Then to find the value on n when g(n)=3

$\begin{gathered} g(n)=\frac{24}{n}=3 \\ n=\frac{24}{3} \\ n=8 \end{gathered}$

So the answer is n=8.0