Question

The equation `P = 1 + d/33` gives the pressure, `P`, in atmospheres (atm) at a depth of `d` feet in the sea. For what depths `d` is the pressure at least 1 atm and at most 7 atm?

Answer 1

`"1 atm" ≤ P ≤ "7 atm"` when `0 ≤ d ≤ "200 ft"`.

Explanation:

The formula is

`color(blue)(bar(ul(|color(white)(a/a) P = 1 + d/33color(white)(a/a)|)))" "`

We can do some rearranging to get:

`33P = 33 + d`

`d = 33P - 33`

`color(blue)(bar(ul(|color(white)(a/a) d = 33(P - 1)color(white)(a/a)|)))" "`

When `P = "1 atm"`,

`d = 33(1 - 1) = 33×0 = 0`

When `P = "7 atm"`,

`d = 33(7 - 1) = 33×6 = "200 ft"` (2 significant figures)

∴ The pressure is at least 1 atm and at most 7 atm when the depth ranges from 0 ft to 200 ft.