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Underwater pressure. At sea level, the weight of the atmosphere exerts a pressur

ID: 2881560 • Letter: U

Question

Underwater pressure. At sea level, the weight of the atmosphere exerts a pressure of 14.7 pounds per square inch, commonly referred to as 1 atmosphere of pressure. As an object descends in water, pressure P and depth d are linearly related. In salt water, the pressure at a depth of 33 ft is 2 atms, or 29.4 pounds per square inch. Find a linear model that relates pressure P (in pounds per square inch) to depth d (in feet). Interpret the slope of the model. Find the pressure at a depth of 50 ft. Find the depth at which the pressure is 4 atms. Underwater pressure. Refer to Problem 3. In fresh water, the pressure at a depth of 34 ft is 2 atms, or 29.4 pounds per square inch. Find a linear model that relates pressure P (in pounds per square inch) to depth d (in feet). Interpret the slope of the model. Find the pressure at a depth of 50 ft. Find the depth at which the pressure is 4 atms.

Explanation / Answer

(A) The linear model is y = mx + c

29.4 = 14.7 + 33m

Solving, m = 0.4455

The modek is y = 0.4455x + 14.7

(B) The slope 0.4454 means for every one foot depth, the atmospheric pressure increases by 0.4455 psi

(C) y = 0.4455(50) + 14.7 = 36.98 psi

(D) 4 atm = 58.8 psi

58.8 = 0.4455x + 14.7

Solving, x = 98.99 ft