Chapter 10 Resource Masters PDF Study Guide and Intervention Workbook.

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9-4 Study Guide and Intervention (continued). Common Logarithms. Change of Base Formula The following formula is used to change expressions with.

Study Guide and Intervention

6 11. 10. 12 6 3 2(4) 6. 11. 14 (8 20 2). 7. 12. 6(7) 4 4 5 38. 13. 8(42 Study Guide and Intervention (continued) ... Properties of Logarithms.

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9-2 Study Guide and Intervention (continued). Logarithms and Logarithmic Functions. Solve Logarithmic Equations and Inequalities. If b > 1 x > 0

7-6 Study Guide and Intervention

7-6 Study Guide and Intervention. Growth and Decay. NAME. Exponential Growth. Exponential Growth Population increases and growth of monetary investments are

Chapter 10: Exponential and Logarithmic Relations

Solve exponential equations and inequalities using common logarithms. Study Guide and Intervention CRM pp. 573–574

3-3 Study Guide and Intervention - Properties of Logarithms

3-3 Study Guide and Intervention Properties of Logarithms Since logarithms and exponents have an inverse relationship ... log (a – 2) + 6 log (b + 4) –.

Chapter 10 Resource Masters

Study Guide and Intervention Workbook. 0-07-828029-X 1 2 3 4 5 6 7 8 9 10 066 11 10 09 08 07 06 05 04 03 02 ... common logarithm. LAW·guh·RIH·thuhm.

Study Guide and Intervention

Common Logarithms Base 10 logarithms are called common logarithms. The expression log. 10 x is usually written without the subscript as log x. Use the LOG.

Read PDF Study Guide And Intervention Functions

Aug 25 2565 BE 2-6 Study Guide and Intervention Special ... NAME DATE PERIOD 7-3 Study Guide and Intervention ... the dependent variable

Chapter 7 Resource Masters

Study Guide and Intervention Workbook 1 2 3 4 5 6 7 8 9 DOH 16 15 14 13 12 11. PDF Pass ... Multiplication Properties of Exponents. Study Guide and ...

Chapter 10 Resource Masters

Study Guide and Intervention

Exponential Functions

NAME ______________________________________________ DATE ____________ PERIOD _____

10-110-1

©Glencoe/McGraw-Hill573Glencoe Algebra 2

Lesson 10-1

Exponential FunctionsAn exponential functionhas the form yab x where a0,b0, and b1.

1.The function is continuous and one-to-one.

Properties of an2.

The domain is the set of all real numbers.

Exponential Function3.

The x-axis is the asymptote of the graph.

4.The range is the set of all positive numbers if a0 and all negative numbers if a0.

5.The graph contains the point (0, a).

Exponential GrowthIf a0 and b1, the function yab

x represents exponential growth. and DecayIf a0 and 0 b1, the function yab x represents exponential decay.

Sketch the graph of y0.1(4)

x .Then state the function's domain and range. Make a table of values. Connect the points to form a smooth curve. The domain of the function is all real numbers, while the range is the set of all positive real numbers. Determine whether each function represents exponential growthor decay. a. y0.5(2) x b.y2.8(2) x c.y1.1(0.5) x exponential growth, neither, since 2.8, exponential decay, since since the base, 2, is the value of ais less the base, 0.5, is between greater than 1 than 0. 0 and 1 Sketch the graph of each function. Then state the function's domain and range. 1. y3(2) x 2.y2 x

3.y0.25(5)

Domain: all real Domain: all real Domain: all real numbers; Range: all numbers; Range: all numbers; Range: allpositive real numbers negative real numberspositive real numbers

Determine whether each function represents exponential growth or decay. 4. y0.3(1.2) x growth5.y5 x neither6.y3(10) x decay 4 5 xy O xy O xy O 1 4 x10123 y0.025 0.1 0.4 1.6 6.4 xy O

Example1Example1

Example2Example2

ExercisesExercises

©Glencoe/McGraw-Hill584Glencoe Algebra 2

Enrichment

NAME ______________________________________________ DATE______________ PERIOD _____

10-210-2

Musical Relationships

The frequencies of notes in a musical scale that are one octave apart are related by an exponential equation. For the eight C notes on a piano, the equation is C n C 1 2 n1 ,where C n represents the frequency of note C n

1.Find the relationship between C

1 and C 2

2.Find the relationship between C

1 and C 4 The frequencies of consecutive notes are related by a common ratio r.The general equation is f n f 1 r n1

3.If the frequency of middle C is 261.6 cycles per second

and the frequency of the next higher C is 523.2 cycles per second, find the common ratio r.(Hint:The two C's are 12 notes apart.) Write the answer as a radical expression.

4.Substitute decimal values for rand f

1 to find a specific equation for f n

5.Find the frequency of F

above middle C.

6.Frets are a series of ridges placed across the fingerboard of a guitar. They

are spaced so that the sound made by pressing a string against one fret has about 1.0595 times the wavelength of the sound made by using the next fret. The general equation is w n w 0 (1.0595) n .Describe the arrangement of the frets on a guitar.

Solve Logarithmic EquationsYou can use the properties of logarithms to solve equations involving logarithms.

Solve each equation.

a. 2 log 3 xlog 3 4 log 3 25
2 log 3 xlog 3 4 log 3

25Original equation

log 3 x 2 log 3 4 log 3

25Power Property

log 3 log 3

25Quotient Property

25Property of Equality for Logarithmic Functions

x 2

100Multiply each side by 4.

x10Take the square root of each side. Since logarithms are undefined for x0,10 is an extraneous solution.

The only solution is 10.

b. log 2 xlog 2 (x2) 3 log 2 xlog 2 (x2) 3Original equation log 2 x(x2) 3Product Property x(x2) 2 3

Definition of logarithm

x 2

2x8Distributive Property

x 2

2x 8 0Subtract 8 from each side.

(x4)(x2) 0Factor. x2orx4Zero Product Property Since logarithms are undefined for x0,4 is an extraneous solution.

The only solution is 2.

Solve each equation. Check your solutions.

1. log 5 4 log 5 2xlog 5

2432.3 log

4quotesdbs_dbs5.pdfusesText_10

[PDF] Chapter 10 Resource Masters Study Guide and Intervention Workbook.

Chapter 10

Resource Masters

Study Guide and Intervention

Exponential Functions

10-110-1

©Glencoe/McGraw-Hill573Glencoe Algebra 2

Lesson 10-1

1.The function is continuous and one-to-one.

Properties of an2.

The domain is the set of all real numbers.

Exponential Function3.

The x-axis is the asymptote of the graph.

4.The range is the set of all positive numbers if a0 and all negative numbers if a0.

5.The graph contains the point (0, a).

Exponential GrowthIf a0 and b1, the function yab

Sketch the graph of y0.1(4)

3.y0.25(5)

Example1Example1

Example2Example2

ExercisesExercises

©Glencoe/McGraw-Hill584Glencoe Algebra 2

Enrichment

10-210-2

Musical Relationships

1.Find the relationship between C

2.Find the relationship between C

3.If the frequency of middle C is 261.6 cycles per second

4.Substitute decimal values for rand f

5.Find the frequency of F

6.Frets are a series of ridges placed across the fingerboard of a guitar. They

©Glencoe/McGraw-Hill586Glencoe Algebra 2

Solve each equation.

25Original equation

25Power Property

25Quotient Property

25Property of Equality for Logarithmic Functions

100Multiply each side by 4.

The only solution is 10.

Definition of logarithm

2x8Distributive Property

2x 8 0Subtract 8 from each side.

The only solution is 2.

Solve each equation. Check your solutions.

2432.3 log