chapter 1 12 - 12 El CHAPTER1 FUNCTIONSAND MODELS 9(a F(b...

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Unformatted text preview: 12 El CHAPTER1 FUNCTIONSAND MODELS 9. (a) F (b) The slope of 3; means that F increases 2 degrees for each (100, 212) , 1ncrease of 1 °C. (Equivalently. F increases by 9 when 0 increases by 5 and F decreases by 9 when 0 decreases by 5.) The F-intercept of 32 is the Fahrenheit temperature corresponding to a Celsius temperature of 0. 10. (a) Let d 2 distance traveled (in miles) and t = time elapsed (in hours). At t = 0, d : O and at t : 50minutes : 50- 6—10 2 g h, d: 40. Thus we have two points: (0,0) and (%,40). so _40—0 3—0 (c) The slope is 48 and represents the car’s speed in mi / h. m =48andsodz48t. . . . T2—T1 80—70 10 1 11.aUnN la f dT 1 f, fidthl tb———=———=—=—.S () Slg lnp ceoaran mpaceoywe n esopeo eNa—N1 173—113 60 6 0a linearequationisT—80:%(N;173) 4:) T—80=%N—% c) T=%N+§g—7 [$251.15]. (b) The slope of % means that the temperature in Fahrenheit degrees increases one—sixth as rapidly as the number of cricket chirps per minute. Said differently, each increase of 6 cricket chirps per minute corresponds to an increase of 1 °F. (c) When N : 150, the temperature is given approximately by T = %(150) + 3—21 = 76.15 °F % 76 OF. 12. (a) Let ac denote the number of chairs produced in one day and y the associated cost. Using the points (100, 2200) and (300, 4800) we get the slope 333% : 3%) = 13. So y — 2200 = 13(m — 100) 4:» y 2 1333 -l- 900. (b) The slope of the line in part (a) is 13 and it represents the cost (in dollars) of producing each additional chair. 100 200 300 x (c) The y—intercept is 900 and it represents the fixed daily costs of operating the factory. change m pressure 4'34 # 0434. Using P for pressure and d for depth with the point 10 feet change in depth 10 (d, P) = (0. 15), we have the slope-intercept form of the line, P = 0.434d + 15. 13. (a) We are given (b) When P = 100, then 100 = 0.434d + 15 <=> 0.434d = 85 41) d = 01534 w 195.85 feet. Thus, the pressure is 100 lb/in2 at a depth of approximately 196 feet. ...
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