slide r.1- 1 copyright © 2008 pearson education, inc. publishing as pearson addison-wesley
TRANSCRIPT
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.
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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.
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Slide R.1- 7 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Example 3: Graph y = x2 –1.
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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
Slide R.1- 9 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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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
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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
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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
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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