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

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

$y=18,000/x$

Answer 2

Answer:

$y=\frac{18000}{x}$

Step-by-step 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.

⇒$y \propto \frac{1}{x}$

Let the proportionality be k

So, $y=\frac{k}{x}$  ---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

$600=\frac{k}{30}$

$600 \times 30=k$

$18000 =k$

Substitute the value of k in A

So,  $y=\frac{18000}{x}$

Hence  function can be used to model the volume of the gas y, in cubic inches, when the pressure is x psi is    $y=\frac{18000}{x}$