Prentice Hall Algebra 2

7 Chapter Review

Connecting BIG ideas to the Math You've Learned

1 Modeling The function y equals , eh b to the x , comma   eh greater than 0 comma   b greater than 1 comma  models exponential growth. y equals , eh b to the x  models exponential decay if 0 less than b less than 1 . Exponential Models (Lesson 7-1)
The population P is 1000 at the start. In each time period,
The model of growth rises in a curve from (0, 1,000) through (8, 1,500) at a rate of 1,000 times 1.05 to the t power. The model of decay falls from 1,000 through (16, 500) at a rate of 1,000 times 0.95 to the t power.
P grows by 5%. p equals , 1000 . open , 1.05 , close to the t  
P shrinks by 5%. p equals , 1000 . open , 0.95 , close to the t
Properties of Logarithms (Lesson 7-4) table with 6 rows and 2 columns , row1 column 1 , b to the eh , b to the c , column 2 equals , b super eh plus end super . to the c , row2 column 1 , log base b , m n , column 2 equals , log base b , m plus , log base b , n , row3 column 1 , fraction b to the eh , over b to the c end fraction , column 2 equals . b super eh minus c end super , row4 column 1 , log base b . m over n , column 2 equals , log base b , m minus , log base b , n , row5 column 1 , log base b . m to the n , column 2 equals n , log base b , m , row6 column 1 , log base n , m , column 2 equals . fraction log base b , m , over log base b , n end fraction , end table
2 Equivalence Logarithms are exponents. In fact, log base b   eh equals c  if and only if b to the c , equals eh .    
3 Function The exponential function y equals , b to the x  and the logarithmic function y equals   log base b , x  are inverse functions. Logarithmic Functions as Inverses (Lesson 7-3)
A graph with four logarithmic functions.
Image Long Description
y equals , 2 to the x
y equals , log base 2 , x
y equals . 2 super x minus 1 end super
y equals open , log base 2 , x close plus 1
Exponential and Natural Logarithm Equations (Lessons 7-5 and 7-6)
e super x plus 3 end super . equals 4
e to the x , middle dot , e cubed , equals 4  or x + 3 = ln 4
table with 2 rows and 2 columns , row1 column 1 , e to the x , column 2 equals , fraction 4 , over e cubed end fraction , row2 column 1 , x , column 2 equals l n , fraction 4 , over e cubed end fraction , end table
x equals open ln 4 close minus 3

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Table of Contents

Prentice Hall Algebra 2 Chapter 1 Expressions, Equations, and Inequalities Chapter 2 Functions, Equations, and Graphs Chapter 3 Linear Systems Chapter 4 Quadratic Functions and Equations Chapter 5 Polynomials and Polynomial Functions Chapter 6 Radical Functions and Rational Exponents Chapter 7 Exponential and Logarithmic Functions Chapter 8 Rational Functions Chapter 9 Sequences and Series Chapter 10 Quadratic Relations and Conic Sections Chapter 11 Probability and Statistics Chapter 12 Matrices Chapter 13 Periodic Functions and Trigonometry Chapter 14 Trigonometric Identities and Equations Skills Handbook English/Spanish Illustrated Glossary Selected Answers Index Acknowledgments