Question

If g(n) varies inversely with n and g(n)= 13 when n=2 then find the value of n wheng(n)= 4Round final answer to the tenths place

Answer 1

Recall that y varies inversely with x if and only if exist a constant k such that:

`y=(k)/(x)\text{.}`

Since g(n) varies inversely with n, we can set the following equation:

`g(n)=(k)/(n)\text{.}`

Now, we know that g(n)=13 when n=2, then:

`13=(k)/(2)\text{.}`

Multiplying the above equation by 2 we get:

`\begin{gathered} 13*2=(k)/(2)*2, \\ 26=k\text{.} \end{gathered}`

Therefore:

`g(n)=(26)/(n)\text{.}`

Setting g(n)=4 we get:

`4=(26)/(n)\text{.}`

Multiplying the above equation by n we get:

`\begin{gathered} 4* n=(26)/(n)* n, \\ 4n=26. \end{gathered}`

Dividing the above equation by 4 we get:

`\begin{gathered} (4n)/(4)=(26)/(4), \\ n=6.5. \end{gathered}`

Answer: n=6.5.