At the surface of the ocean, the water pressure is the same as the air pressure above the water... find equation; when depth is 120

Question

At the surface of the ocean, the water pressure is the same as the air pressure above the water, about 15 lb/in^2, Below the surface the water pressure increases by about 4.44 lb/in^2 for every 10 ft of descent.
Write a function f(x) which expresses the water pressure in pounds per square inch as a function of the depth in inches below the ocean surface.

 

f(x)=?

At what depth is the pressure 120 lb/in^2?

Answer 1

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