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Section 2.3 (continued) [Linear] Model Upgrades

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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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slide1

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

slide2

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

slide4

Ironman Triathlon (pages 19, 76-77)

What is the slope of each line?

m = 4

m = 36

m = 10.5

slide5

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)

slide6

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) =

slide7

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

slide8

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 = ???

slide9

Women’s Shoe Size Function

piecewise defined

17 pieces !!(page 75)

slide10

Homework:

Pages 85-87: #45, #47-55

TURN IN: #45, #52, #55 (maple graph)