Question

For a fixed amount of a gas at a constant temperature, the volume of the gas is inversely proportional to its pressure. At a pressure of 30 pounds per square inch (psi), a gas has a volume of 600 in.3. Which function can be used to model the volume of the gas y, in cubic inches, when the pressure is x psi?

Answer 1

`y=(18000)/(x)`

Explanation:

Let the volume of gas be y

Let the pressure be x

Since we are given that the volume of the gas is inversely proportional to its pressure.

⇒
`y \propto (1)/(x)`

Let the proportionality be k

So,
`y=(k)/(x)` ---A

Now we are given that At a pressure of 30 pounds per square inch (psi), a gas has a volume of 600 cubic inches

So, substitute x = 30

y = 600

`600=(k)/(30)`

`600 * 30=k`

`18000 =k`

Substitute the value of k in A

So,
`y=(18000)/(x)`

Hence function can be used to model the volume of the gas y, in cubic inches, when the pressure is x psi is
`y=(18000)/(x)`

Answer 2

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form
`y*x=k` or
`y=k/x`

Let

x-------> the pressure in PSI

y------> the volume of the gas in cubic inches

In this problem we have the point
`(30,600)`

so

`x=30\ psi\\y=600\ in^(3)`

Find the constant k

`y*x=k`

substitute the values of x and y

`600*30=k`

`k=18,000\ lb*in`

the equation is

`y=18,000/x`

therefore

the answer is

`y=18,000/x`