Royal Melbourne Institute of TechnologyECON 1061Quantitative Analysis Notes - Week 1

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Quantitative Analysis Notes – Week 1 Lecture Outline 1. Solving simple equations 2. The rules for indices and simplifying exponential expressions 3. Linear Equations (define the slope and interc... ept of a straight line and plot its graph) 4. Non-linear equations (solve quadratic equations) 5. Linear and non-linear applications in economics Basic Maths (solve the following equations) 1. 3x2 x+5 ÷ 6 x x 2 −25 =8 x 2. x2 + 4x – 6 = 2(2x + 5) 3. √x2−x6 = 2 Solutions (cont.) 1) 3x2 x+5 ÷ 6 x x 2 −25 =8 x 3x2 x+5 × (x−5)(x+5) 6 x =8 x (reason: a2 – b2 = (a - b)(a + b)) 3 x2 ( x−5)=48 x2 x−5=16 Thus x=21 2) x2 + 4x – 6 = 2(2x + 5) X2 + 4x – 6 = 4x + 10 X2 = 16 Therefore x = +4 or -4 3. √x2−x6 = 2 Squaring both sides: 2x x−6 = 4 2x=4 x−2 4 x=12 Indices • These are also known as powers, exponents, and orders. • Are shorthand for repeated multiplications of the same number or variable by itself. • For example, 5 ×5 ×5=53 here, 3 is the index, power, order, or exponent and 5 is the base. The rules for indices 1. (Any number, except zero)0 = 1. For example, 30 = 1, 1000 = 1, and so on. 2. Any number raised to the power of one equals the number itself. For example, 31 = 3, 781 = 78, and so on. 3. am × an = am+n [Show More]

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