Modern scuba-diving equipment allows divers to stay underwater for long periods of time. Underwater instructors use mathematics to explore safety issues related to scuba diving. An instructor gives scuba-diving students the handout shown. A handout with diver's information. At the water surface, the air around a diver exerts 1 atmosphere (A T M) of pressure. Underwater, the pressure P (A T M) around the diver increases. It varies with the diver's depth D, in feet, according to the equation P equals D over 33 all plus 1. The volume Vee of a given amount of air varies inversely with the pressure P around it, so the volume of air in the diver's lungs increases as she ascends. Use the information in the handout. Part A Suppose that a certain amount of air takes up a volume of 4 qt in a diver’s lungs at a depth of 66 ft, where the pressure is 3 atm. As the diver changes depth, the volume taken up by this fixed amount of air changes. Write an equation that defines the volume V, in quarts, taken up by that amount of air at a given depth d, in feet. Explain. Part B Complete the table and graph below to show how the volume of the given amount of air in the diver’s lungs varies with depth. What are the asymptote(s) of your graph, and how do they apply to the real-world situation? A handout titled diver's information. First bullet: at the water surface, the air around a diver exerts one atmosphere, A T M, of pressure. Second bullet: underwater, the pressure P in A T Ms around the diver increases. It varies with the divers depth dee, in feet, according to the equation, P equals d over 33, plus 1. Third bullet: the volume Vee of a given amount of air varies inversely with the pressure P around it, so the volume of air in the diver's lungs increases as she ascends. Depth (ft) Volume (qt) 0 33 66 99 132 165