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Welcome to Pre-Calculus!! College-Prep Class Grades are “curved” ▫ A 88 – 100% B 78 – 87% C 65 – 77% D 55 – 64% F Below 54% Tests = 80% of grade HW = 10% Quizzes, Notes, etc = 10% HW every night (almost) ▫ pencil ▫ ALL work shown 80% HW drop low test (It’s difficult!!) Posted on website Late HW = ½ credit up until date of test

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Supplies 3-ring binder or Spiral Notebook for notes Paper (Lined & Graph) Pencils!! Scientific Calculator (TI-30XIIS) Graphing Calculator (TI-84 or free online utilities) Come study with me every day (almost) after school!!

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1.1 Intro to Modeling

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Mathematical Model: a mathematical representation of some aspect of a real world system Slope of a line: Given 2 points: (x 1, y 1 ) and (x 2, y 2 ) x 1 ≠ x 2 Eqtns of line: Slope-int form: y = mx + b Point-slope form:y – y 1 = m(x – x 1 )

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Ex 1) Find proper dosage, to nearest tenth of mL, for child weighing 39 lbs, given the recommended dosages: Plot pts to see if can assume it’s linear Choose 2 pts to find slope (15, 0.5) and (27, 0.9) Use point-slope form: Body weight x (lb)152733465265 Dosage y (mL)0.50.91.11.51.72.2 Check: 39 lb weight:

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Quadratic Function: Ex 2) Find a model that relates Surface Area (A) to body weight (x) Plot pts Parabola Quadratic Body weight x (lb)038152024 Surface Area A (m 2 )00.130.240.360.440.50 (Graph is a parabola) (0, 0) to find c c = 0

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Ex 2 cont. 0.24 = 64a + 8b 0.50 = 576a + 24b Choose 2 pts (8, 0.24) & (24, 0.50) 0.24 = a(8) 2 + b(8) 0.50 = a(24) 2 + b(24) ( )(–3) –0.72 = –192a – 24b 0.50 = 576a + 24b –0.22 = 384a –0.00057292… = a use STO on calc – don’t round until last step!

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Ex 2 cont. 0.24 = 64(–0.00057292…) + 8b 0.03458333… = b Round ‘a’ and ‘b’ to 5 decimal places & plug into A = ax 2 + bx: A = –0.00057x 2 + 0.03458x Plug in other pts to check accuracy Plug STO value into ‘a’ & solve for ‘b’

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Ex 3) Find eqtn for earnings per share in terms of debts/assets ratio Plot pts quadratic y = ax 2 + bx + c Plug in 3 pts to get a system of 3 eqtns (0, 1.60), (10, 1.85), (20, 2.00) 1.60 = a(0) 2 + b(0) + c 1.85 = a(10) 2 + b(10) + c 2.00 = a(20) 2 + b(20) + c Debts/assets x (%)01020304050607080 Earnings per share y ($)1.601.852.002.202.302.252.101.801.60 c = 1.60 1.85 = 100a + 10b + 1.60 2.00 = 400a + 20b + 1.60

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Ex 3 cont. c = 1.60 1.85 = 100a + 10b + 1.60 2.00 = 400a + 20b + 1.60 0.25 = 100a + 10b 0.40 = 400a + 20b ( )(–2) –0.50 = –200a – 20b 0.40 = 400a + 20b –0.10 = 200a –0.0005 = a 0.25 = 100(–0.0005) + 10b 0.03 = b y = –0.0005x 2 + 0.03x + 1.60

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Ex 4) Test model for debts/assets ratio of 60% From Ex 3: y = –0.0005x 2 + 0.03x + 1.60 Plug 60 into x: y = –0.0005(60) 2 + 0.03(60) + 1.60 y = 1.60 How accurate is our model?

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Homework #101 Pg. 8 1 – 11 odd, 12, 14 – 17, 25

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