Section 6 3 Formulas Copyright 2013 2010 2007

Section 6. 3 Formulas Copyright 2013, 2010, 2007, Pearson, Education, Inc.

What You Will Learn Formulas Evaluating a Formula Solving for a Variable in a Formula 6. 3 -2 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Definitions A formula is an equation that typically has a real-life application. To evaluate a formula, substitute the given values for their respective variables and then evaluate using the order of operations. 6. 3 -3 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 1: Simple Interest The simple interest formula, interest = principal × rate × time, or i = prt, is used to find the interest you must pay on a simple interest loan when you borrow principal, p, at simple interest rate, r, in decimal form, for time, t. 6. 3 -4 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 1: Simple Interest Chris Campbell borrows $5000 at a simple interest rate of 6. 5% for 3 years. a) How much will Chris Campbell pay in interest at the end of 3 years? b) What is the total amount he will repay the bank at the end of 3 years? 6. 3 -5 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 1: Simple Interest a) How much will Chris Campbell pay in interest at the end of 3 years? Solution p = $5000, r = 6. 5%, t = 3 Chris must pay $975 in interest. 6. 3 -6 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 1: Simple Interest What is the total amount he will repay the bank at the end of 3 years? Solution The total he must pay at the end of 3 years is the principal, $5000, plus the $975 interest, for a total of $5975. 6. 3 -7 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 2: Volume of an Ice-Cream Box The formula for the volume of a rectangular box is volume = length × width × height, or V = lwh. Use the formula V = lwh to find the width of a rectangular box of ice cream if l =7 in. , h =3. 5 in. , and V =122. 5 in 3. 6. 3 -8 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 2: Volume of an Ice-Cream Box l =7 in. , h =3. 5 in. , and V =122. 5 in 3 Solution The width of the ice-cream box is 5 in. 6. 3 -9 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Mathematical Models When we represent real phenomena, such as finding simple interest, mathematically we say we have created a mathematical model or simply a model to represent the situation. A model may be a single formula, an equation, or a system of many equations. 6. 3 -10 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Greek Letters Many formulas contain Greek letters, such as μ (mu), σ (sigma), Σ (capital sigma), δ (delta), Δ (capital delta), 6. 3 -11 ε (epsilon), π (pi), θ (theta), and λ (lambda). Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 3: A Statistics Formula A formula used in the study of statistics to find a standard score (or z -score) is Find the value of z. when μ = 100, σ = 16, n = 4. 6. 3 -12 Copyright 2013, 2010, 2007, Pearson, Education, Inc. = 120,

Example 3: A Statistics Formula Solution = 120, μ = 100, σ = 16, n = 4. 6. 3 -13 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Subscripts Some formulas contain subscripts. Subscripts are numbers (or letters) placed below and to the right of variables. For example, if two different amounts are used in a problem, they may be symbolized as A and A 0 (read “A sub zero” ), or A 1 (read “A sub one”) and A 2 (read “A sub two”). 6. 3 -14 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Solving for a Variable in a Formula or Equation You are given a formula or an equation expressed in terms of one variable and asked to express it in terms of a different variable. To do so, treat each of the variables, except the one you are solving for, as if it were a constant. Then solve for the variable desired. 6. 3 -15 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 4: Solving for a Variable in an Equation Solve the equation 2 x + 5 y – 10 = 0 for y. Solution 6. 3 -16 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 4: Solving for a Variable in an Equation Solution 6. 3 -17 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 4: Solving for a Variable in an Equation Solution The equation is solved for y: The solution can also be expressed in the form This form is convenient for graphing linear equations. 6. 3 -18 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 5: Solving for a Variable in a Formula An important formula used in statistics is Solve this equation for x. 6. 3 -19 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 5: Solving for a Variable in a Formula Solution or 6. 3 -20 Copyright 2013, 2010, 2007, Pearson, Education, Inc.