1 / 10

Understanding Piecewise-Defined Functions in Linear Models: Ironman Triathlons and Depreciation

This section covers the concept of piecewise-defined functions within linear models, illustrating their application through examples such as Ironman Triathlon performance analysis and a DJ system's depreciation. It outlines the results for a triathlon participant across three legs with calculated speeds and formulas, including a piecewise model. Additionally, it features a women’s shoe size function, exploring both functional modeling and graphing techniques. Engage with exercises to deepen your understanding of these concepts.

keegan
Download Presentation

Understanding Piecewise-Defined Functions in Linear Models: Ironman Triathlons and Depreciation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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)

More Related