Question

At the surface of the ocean the water pressure is the same as the air pressure above the water, 15 lb/in2. Below the surface the water pressure increases by 4.34 lb/in2 for every 10 ft of descent. Find an equation for the relationship between pressure (P, in lb/in2) and depth (d, in ft) below the ocean surface.

Answer 1

Step-by-step explanation:

f(x) = mx + b, where m is the slope and b is the y-intercept

You are given m = 4.44 (lb/in^2) for every 10 ft of descent, but you want f(x) to be a function of the depth in inches, so you must find what m is for every inch of descent.  

10 ft *(12 in/ft) = 120 inches

So m = 4.44 every 120 inches of descent, therefore

m = 4.44 / 120 = 0.037 every inch of descent

So f(x) = 0.037x + b

To find b, use the fact that f(0) = 15, thus b = 15

So the equation is f(x) = 0.037x + 15

To find when the pressure is 120, set f(x) = 120 and solve for x

120 = 0.037x + 15

0.037x = 105

x = 105 / 0.037 = 2837.8 inches, which is about 236.5 ft