# 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?

Jan 7, 2017

$\text{1 atm" ≤ P ≤ "7 atm}$ when 0 ≤ d ≤ "200 ft".

#### Explanation:

The formula is

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} P = 1 + \frac{d}{33} \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

We can do some rearranging to get:

$33 P = 33 + d$

$d = 33 P - 33$

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} d = 33 \left(P - 1\right) \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

When $P = \text{1 atm}$,

d = 33(1 - 1) = 33×0 = 0

When $P = \text{7 atm}$,

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.