1. Slide R.1- 1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

2. Graphs and Equations OBJECTIVES  Graph equations.  Use the graphs as mathematical models to make predictions.  Carry out calculations involving compound interest. R.1

3. Slide R.1- 3 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley DEFINITION: The graph of an equation is a drawing that represents all ordered pairs that are solutions of the equation. R.1 Graphs and Equations

4. Slide R.1- 4 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 1: Graph y = 2x + 1. We first find some ordered pairs that are solutions and arrange them in a table. R.1 Graphs and Equations

5. Slide R.1- 5 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 2: Graph 3x + 5y = 10. First solve this equation for y. R.1 Graphs and Equations

6. Slide R.1- 6 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 2 (concluded): Then, we will find three ordered pairs (choosing multiples of 5 to avoid fractions) and use them to sketch the graph. R.1 Graphs and Equations

7. Slide R.1- 7 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 3: Graph y = x 2 –1. R.1 Graphs and Equations

8. Slide R.1- 8 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 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. R.1 Graphs and Equations

9. Slide R.1- 9 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley R.1 Graphs and Equations Example 5: The graph below shows the numbers of digital photos printed at home from 2000 to 2006.

10. Slide R.1- 10 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley R.1 Graphs and Equations Example 5 (continued): Use the model h = 0.7t + 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

11. Slide R.1- 11 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 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.

12. Slide R.1- 12 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 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.

13. Slide R.1- 13 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 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

14. Slide R.1- 14 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 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.