At the surface of the ocean the water pressure is the same a

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 4.84 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 70 lb/in^2 ? Include the units in your answer:

Solution

The water pressure increases by 4.84 lb/ in² for every 10 ft. of descent below the ocean surface . Thus, f (x) which expresses the water pressure as a function of depth below the ocean surface is a linear function. Let f (x) = ax + b. where a and b are constants and x is the depth below the ocean surface. Since f ( x) = 15, when x = 0, we have 15 = a*0 + c so that c = 15. Then f (x) = ax + 15. Further, when x = 10, f (x) = 15 + 4.84 = 19.84 . Therefore, 19.84 = 10a + 15 or, 10a = 19.84 - 15 = 4.84 so that x = 4.84/10 = 0.484. Then, f (x) = 0.484x + 15. When f (x) = 70, we have 0.484x + 15 = 70 or, 0.484x = 70 - 15 = 55 so that x = 55/ 0.484 = 113.6364 = 113.64 ft ( approximately on rounding off to 2 decimal places) = 113 ft, 7.64 inches ( approx). Thus, the pressure is 70 lb/in² at a depth of 113.64 ft.