122 CHAPTER 1 Equations and Inequalities 42. Warehouse Club Membership Suppose that the annual fee for a warehouse club membership is $50 and that the reward rate on club purchases for the year is 1.6%. Then the actual annual cost of a membership y, in dollars, for an amount of annual club purchases x, in dollars, can be modeled by the following linear equation. y = 50 - 0.016x (a) Determine the actual annual cost of the membership if club purchases for the year are $1500. (b) What amount of club purchases would reduce the actual annual cost of the membership to $0? (c) If club purchases for the year exceed $3125, how is the actual annual membership cost affected? 43. Indoor Air Pollution Formaldehyde is an indoor air pollutant formerly found in plywood, foam insulation, and carpeting. When concentrations in the air reach 33 micrograms per cubic foot 1mg>ft32, eye irritation can occur. One square foot of new plywood could emit 140 mg per hr. (Data from A. Hines, Indoor Air Quality & Control.) (a) A room has 100ft2 of new plywood flooring. Find a linear equation F that computes the amount of formaldehyde, in micrograms, emitted in x hours. (b) The room contains 800ft3 of air and has no ventilation. Determine how long it would take for concentrations to reach 33mg>ft3. (Round to the nearest tenth.) 44. Classroom Ventilation According to the American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (ASHRAE), a nonsmoking classroom should have a ventilation rate of 15 ft3 per min for each person in the room. (a) Write an equation that models the total ventilation V (in cubic feet per hour) necessary for a classroom with x students. (b) A common unit of ventilation is air change per hour (ach). One ach is equivalent to exchanging all the air in a room every hour. If x students are in a classroom having volume 15,000ft3, determine how many air exchanges per hour (A) are necessary to keep the room properly ventilated. (c) Find the necessary number of ach (A) if the classroom has 40 students in it. (d) In areas like bars and lounges that allow smoking, the ventilation rate should be increased to 50ft3 per min per person. Compared to classrooms, ventilation should be increased by what factor in heavy smoking areas? 45. College Enrollments The graph shows the projections for total undergraduate enrollment at degree-granting institutions from fall 2020 to fall 2027. 15.0 15.5 16.0 16.5 17.0 17.5 18.0 ’20 ’21 ’22 ’23 ’27 ’24 ’25 ’26 Enrollments at Degree-Granting Institutions Enrollment (in millions) Year Data from U.S. Department of Education, National Center for Education Statistics. 17.1 17.1 17.1 17.2 17.2 17.3 17.4 17.4 The following linear model provides the approximate enrollment, in millions, between the years 2020 and 2027, where x = 0 corresponds to 2020, x = 1 to 2021, and so on, and y is in millions of students. y = 0.04917x + 17.06
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