Copyright 2008 Pearson Education Inc Publishing as Pearson
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 1
R. 1 Graphs and Equations OBJECTIVES Ø Graph equations. Ø Use the graphs as mathematical models to make predictions. Ø Carry out calculations involving compound interest. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
R. 1 Graphs and Equations DEFINITION: The graph of an equation is a drawing that represents all ordered pairs that are solutions of the equation. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 3
R. 1 Graphs and Equations Example 1: Graph y = 2 x + 1. We first find some ordered pairs that are solutions and arrange them in a table. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 4
R. 1 Graphs and Equations Example 2: Graph 3 x + 5 y = 10. First solve this equation for y. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5
R. 1 Graphs and Equations Example 2 (concluded): Then, we will find three ordered pairs (choosing multiples of 5 to avoid fractions) and use them to sketch the graph. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 6
R. 1 Graphs and Equations Example 3: Graph y = x 2 – 1. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 7
R. 1 Graphs and Equations Example 4: Graph x = y 2. In this case, x is expressed in terms of the variable y. Thus, we first choose numbers for y and then compute x. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 8
R. 1 Graphs and Equations Example 5: The graph below shows the numbers of digital photos printed at home from 2000 to 2006. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 9
R. 1 Graphs and Equations Example 5 (continued): Use the model h = 0. 7 t + 0. 3, where t is the number of years after 2000 and h is the number of digital photos printed at home, in billions, to predict the number of digital photos printed at home in 2008. Since 2008 is 8 years after 2000, we substitute, using t = 8. h = 0. 7 · 8 + 0. 3 = 5. 9 billion digital photos Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 10
R. 1 Graphs and Equations THEOREM 1 If an amount P is invested at interest rate i, expressed as a decimal and compounded annually, in t years it will grow to an amount A given by A = P(1 + i)t. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 11
R. 1 Graphs and Equations Example 6: Suppose that $1000 is invested at 8%, compounded annually. How much is in the account at the end of 2 yr? There is $1166. 40 in the account after 2 years. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 12
R. 1 Graphs and Equations THEOREM 2 If a principal P is invested at interest rate i, expressed as a decimal and compounded n times a year, in t years it will grow to an amount A given by Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 13
R. 1 Graphs and Equations Example 7: Suppose that $1000 is invested at 8%, compounded quarterly. How much is in the account at the end of 3 yr? There is $1268. 24 in the account after 3 years. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 14
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