Math........(Graph).

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wbryvmk3

Mathematics

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ACTIVITY 1: GRAPHING Scuba divers must learn about pressure under water. At the water's surface, air exerts 1 atmosphere (atm) of pressure. Under water, the pressure increases. The pressure P (atm) varies d with depth d (A) according to the equation P = 33+ 1. Boyle's law states that the volume V of air varies inversely with the pressure P. If you hold your breath, the volume of air in your lungs increases as you ascend. If you have 4 qt of air in your lungs at a depth of 66 ft (P = 3 atm), the air will expand to 6 qt when you reach 33 ft, where P = 2 atm. 2) Write an equation that represents Boyle's law (the volume of air varies inversely with the pressure). Use k for the variation constant. 3) Solve for k utilizing the fact that you have 4 quarts of air in your lungs when the pressure is 3 atm and 6 quarts of air in your lungs when the pressure is 2 atm. Rewrite your inverse variation equation from Question #2 using your new value for k. 4) Using your equation from Question #3, construct a table relating the volume of air in your lungs to the pressure. The values for the pressures are 1 atm, 2 atm, and 3 atm. 5) Write an equation relating volume to depth. (Hint: Replace Pin your equation from Question #3 with an expression in terms of d. You do not need to simplify your equation.) 6) Using your new equation, make a table to show how the volume of air in your lungs varies with the depth. Set up your table as you would an x/y chart. Let d, the depth, be the independent variable and V, the volume, be the dependent variable. Use these values for d: 99, 66, 33, and 0 (you would be at the water's surface when d = 0). 7) Graph the data from your chart above. Use reasonable units for d and remember to make d the x-axis. ACTIVITY 2: WRITING In Activity 1, you found that the volume of air in a diver's lungs could more than double as the diver resurfaces. This expansion can cause the membranes of the lungs to rupture. Divers must learn to exhale properly while ascending. 8) Write an explanation of why a beginning diver is told not to hold his breath. Refer to tables &|| graphs.
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