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Section 2.3 (continued) [Linear] Model Upgrades

Section 2.3 (continued) [Linear] Model Upgrades . Piecewise-defined functions. Functions that are defined in several pieces: Ironman Triathlon Jason’s DJ System Women’s Shoe Size Function. Ironman Triathlon (pages 19, 76-77) 4K swim, 180K bike, 42K mile run.

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Section 2.3 (continued) [Linear] Model Upgrades

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  1. Section 2.3 (continued) [Linear] Model Upgrades Piecewise-defined functions Functions that are defined in several pieces: Ironman Triathlon Jason’s DJ System Women’s Shoe Size Function

  2. Ironman Triathlon (pages 19, 76-77) 4K swim, 180K bike, 42K mile run The table below summarizes the triathlon results for one participant. • Assumptions for triathlon model: • constant speed during each leg. • no time lapse between legs. LEG 1: (4-0)/(1-0) = 4 km/hr LEG 2: (184-4)/(6-1) = 36 km/hr LEG 3: (226-184)/(10-6) = 10.5 km/hr

  3. Ironman Triathlon (pages 19, 76-77)

  4. Ironman Triathlon (pages 19, 76-77) What is the slope of each line? m = 4 m = 36 m = 10.5

  5. Ironman Triathlon (pages 19, 76-77) What is the formula for each line? S(t) = 4*t B(t) = 4 + 36*(t-1) R(t) = 184 + 10.5*(t-6)

  6. Ironman Triathlon (pages 19, 76-77) What is the formula for the triathlon model? PIECEWISE 4*t for 0 ≤ t ≤ 1 4 + 36*(t-1) for 1 < t ≤ 6 184 + 10.5*(t-6) for 6 < t ≤ 10 T(t) =

  7. 3000*(.80)t 0 ≤ t ≤ 8.5 3000 – 300*t 8.5 < t ≤ 10 J(t) = Jason’s $3000 DJ System Linear Depreciation: L(t) = 3000 – 300*t Double Declining Depreciation: D(t) = 3000*(.80)t Jason’s Best (Tax) Depreciation Model PIECEWISE

  8. Women’s Shoe Size Function w(x) = 3x – 21 domain (continuous): 8.67 ≤ x ≤ 11.33 range (discrete): {5, 5.5, 6, 6.5, 7, 7.5, 8, 8.5, 9, 9.5, 10, 10.5, 11, 11.5, 12, 12.5, 13} What is wrong with this graph? when x = 9 ¾, y = ???

  9. Women’s Shoe Size Function piecewise defined 17 pieces !!(page 75)

  10. Homework: Pages 85-87: #45, #47-55 TURN IN: #45, #52, #55 (maple graph)

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