Single Variable Calculus, Chapter 1, 1.2, Section 1.2, Problem 17

It is known that at the surface of the ocean, the water pressure is the same as the air pressure above the water having a value of $15 \, lb/in^2$. Below the surface, the water pressure increases by $4.34 \, lb/in^2$ for every 10 ft of descent


a.) Express the water pressure as a function of the depth below the ocean surface.




$
\begin{equation}
\begin{aligned}
P &= \displaystyle \frac{4.34}{10} \, d + 15 \text{ where}:\\
P &= \text{pressure in } \displaystyle \frac{lb}{in^2}\\
d &= \text{depth in ft}
\end{aligned}
\end{equation}
$


b.) At what depth is the pressure $100 \, lb/in^2$?


$
\begin{equation}
\begin{aligned}
\text{if } P &= 100,\\
100 &= \displaystyle \frac{4.34}{10} \, d + 15\\
d &= 195.85 \text{ft}\\
d &\approx 196 \text{ft}
\end{aligned}
\end{equation}
$