306 CHAPTER 6 Algebra, Graphs, and Functions Evaluating Formulas 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 given in Section 6.1. Many of the formulas given in this section are discussed in greater detail in other parts of the book. Our first example involves the simple interest formula, which we will study further in Section 10.2. Formulas and Modeling SECTION 6.2 LEARNING GOAL Upon completion of this section, you will be able to: 7 Evaluate a formula. 7 Solve for a variable in a formula or equation. Mateo received a holiday bonus of $3000 at work. He wishes to invest his money in a certificate of deposit to help save for a new boat. In this section, we will use a special kind of equation, called a formula, to determine the amount of interest that Mateo will earn from the certificate of deposit. Why This Is Important Formulas are used in many applications, especially financial applications, that affect our lives. Included in these applications are interest earned on investments as well as interest charged on loans. Understanding how to use formulas may improve our financial literacy and enable us to make better financial decisions. Concept/Writing Exercises 81. Explain why − = ( 1) 1 n for any even number n. * 82. Does + = + x y x y ( ) ? 2 2 2 Complete the table and state your conclusion. x y + ( )2 x y + 2 2 x y 2 3 −2 −3 −2 3 2 −3 The two expressions are not equal. 83. Suppose n represents any natural number. Explain why 1n equals 1. = 1 1 n for all natural numbers because 1 multiplied by itself any number of times will always be 1. 84. a) Explain why −x2 will always be a negative number for any nonzero real number selected for x. Answers will vary. b) Explain why −x ( )2 will always be a positive number for any nonzero real number selected for x. Answers will vary. Challenge Problem/Group Activity 85. Depth of a Submarine The pressure, P, in pounds per square inch (psi) exerted on an object x ft below the sea is given by the equation = + P x 14.70 0.43 . The 14.70 represents the weight in pounds of the column of air (from sea level to the top of the atmosphere) standing over a 1 in. by 1 in. square of seawater. The x 0.43 represents the weight in pounds of a column of water 1 in. by 1 in. by x ft (see Fig. 6.1). This column of air weighs 14.70 lb This column of water weighs 0.43x lb 1 in. by 1 in. square x ft Figure 6.1 a) A submarine is built to withstand a pressure of 148 psi. How deep can that submarine go? 310 ft b) If the pressure gauge in the submarine registers a pressure of 128.65 psi, how deep is the submarine? 265 ft below sea level Research Activities 86. Exponents When were exponents first used? Write a paper explaining how exponents were first used and when mathematicians began writing them in the present form. 87. Ancient Equations Write a report explaining how the ancient Egyptians used equations. Include in your discussion the forms of the equations used. *See Instructor Answer Appendix Brenda Carson/Shutterstock
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