Section 6.2 Formulas

What You Will Learn Upon completion of this section, you will be able to: Evaluate a formula. Solve for a variable in a formula or equation.

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.

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.

Example 1: Simple Interest Fatima borrows $4000 at a simple interest rate of 2.9% for 3 years. a) How much will Fatima pay in interest at the end of 3 years? b) What is the total amount she will repay the bank at the end of 3 years?

Example 1: Simple Interest a) How much will Fatima pay in interest at the end of 3 years? Solution p = $4000, r = 2.9%, t = 3 Thus, Fatima must pay $348 interest.

Example 1: Simple Interest b) What is the total amount she will repay the bank at the end of 3 years? Solution The total she must pay at the end of 3 years is the principal, $4000, plus the $348 interest, for a total of $4348.

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 in3.

Example 2: Volume of an Ice-Cream Box l =7 in., h =3.5 in., and V =122.5 in3 Solution The width of the ice-cream box is 5 in.

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 formula, a single equation, or a system of many equations.

μ (mu), σ (sigma), Σ (capital sigma), δ (delta), Δ (capital delta), Greek Letters Many formulas contain Greek letters, such as μ (mu), σ (sigma), Σ (capital sigma), δ (delta), Δ (capital delta), ε (epsilon), π (pi), θ (theta), and λ (lambda).

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 = 120, μ = 100, σ = 16, n = 4.

Example 3: A Statistics Formula Solution = 120, μ = 100, σ = 16, n = 4.

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 A0 (read “A sub zero” ), or A1 (read “A sub one”) and A2 (read “A sub two”).

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.

Example 4: Solving for a Variable in an Equation Solve the equation 2x + 5y –10 = 0 for y. Solution

Example 4: Solving for a Variable in an Equation Solution