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

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

Graphs and Equations

OBJECTIVES Graph equations. Use the graphs as mathematical

models to make predictions. Carry out calculations involving

compound interest.

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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

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

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

3x 5y 10

5y 3x 10

y 3

5x 2

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

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Example 3: Graph y = x2 –1.

R.1 Graphs and Equations

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

Example 4: Graph x = y2.

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

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R.1 Graphs and Equations

Example 5: The graph below shows the numbers of digital photos printed at home from 2000 to 2006.

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

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

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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.

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.

A 1000(1 0.08)2

1000(1.08)2

$1166.40

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

A P 1i

n

nt

.

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.

A 1000 10.08

4

43

1000(1.02)12

$1268.24