Question

If g(n) varies inversely with n and g(n)= 11 when n=2 then find the value of n wheng(n)= 8Round final answer to the tenths place. If answer is a whole number then put a zeroin the tenths place before entering your answer. Work must be shown

Answer 1

Given:

g(n) varies inversely with n

so,

`\begin{gathered} g(n)\propto(1)/(n) \\ g(n)=(k)/(n) \end{gathered}`

Where (k) is the proportionality constant

We will find the value of (k) using the given condition

When n = 2, g(n) = 11

Substitute with n and g(n)

`11=(k)/(2)\rightarrow k=22`

So, the relation between g(n) and (n) will be:

`g(n)=(22)/(n)`

We will find the value of (n) when g(n) = 8

So, substitute with g(n):

`\begin{gathered} 8=(22)/(n) \\ \\ n=(22)/(8)=2.75 \end{gathered}`

Rounding the answer to the nearest tenth

so, the answer will be:

`n=2.8`