Year 11 Exponential functions and logarithms Page 1 of 28

CAMBRIDGE TECHNOLOGY IN MATHS

Year 11

Exponential functions and logarithms CONTENTS Example: Solving exponential equations 2 Example: Solving exponential inequations 3 Questions on solving exponential functions using a CAS calculator Examples: Graphing exponential functions 5 Questions on graphing exponential functions using a CAS calculator Evaluating logarithms using a CAS calculator 11 Examples: Graphs of y = loga x, where a > 1 13 Questions on graphing logarithmic functions using a CAS calculator Graphing sets of logarithms using a CAS calculator 20 Fitting data using a CAS calculator 22 Example: Graphing data from a table 24 Modelling exponential growth using a CAS calculator 26 Answers 27

Published in: Cambridge Queensland Mathematics B Year 11 © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

Cambridge University Press

Year 11 Exponential functions and logarithms Page 2 of 28

Example: Solving exponential equations

Original location: Ch 3 Example 10, 12 (p.103-105), Ex 3C Q5, 7-9 (p.106) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

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Year 11 Exponential functions and logarithms Page 3 of 28

Example: Solving exponential inequations

Original location: Ch 3 Example 10, 12 (p.103-105), Ex 3C Q5, 7-9 (p.106) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

Cambridge University Press

Year 11 Exponential functions and logarithms Page 4 of 28

Questions on solving exponential functions using a CAS calculator

Original location: Ch 3 Example 10, 12 (p.103-105), Ex 3C Q5, 7-9 (p.106) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

Cambridge University Press

Year 11 Exponential functions and logarithms Page 5 of 28

Examples: Graphing exponential functions

Original location: Ch 3 Example 16, 18 (p.109-116), Ex 3D Q1-4 (p.116) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

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Year 11 Exponential functions and logarithms Page 6 of 28

Original location: Ch 3 Example 16, 18 (p.109-116), Ex 3D Q1-4 (p.116) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

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Year 11 Exponential functions and logarithms Page 7 of 28

Original location: Ch 3 Example 16, 18 (p.109-116), Ex 3D Q1-4 (p.116) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

Cambridge University Press

Year 11 Exponential functions and logarithms Page 8 of 28

Original location: Ch 3 Example 16, 18 (p.109-116), Ex 3D Q1-4 (p.116) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

Cambridge University Press

Year 11 Exponential functions and logarithms Page 9 of 28

Original location: Ch 3 Example 16, 18 (p.109-116), Ex 3D Q1-4 (p.116) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

Cambridge University Press

Year 11 Exponential functions and logarithms Page 10 of 28

Questions on graphing exponential functions using a CAS calculator

Original location: Ch 3 Example 16, 18 (p.109-116), Ex 3D Q1-4 (p.116) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

Cambridge University Press

Year 11 Exponential functions and logarithms Page 11 of 28

Evaluating logarithms using a CAS calculator

Original location: Ch 3 Example 25 (p.122-123, 125) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

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Year 11 Exponential functions and logarithms Page 12 of 28

Original location: Ch 3 Example 25 (p.122-123, 125) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

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Year 11 Exponential functions and logarithms Page 13 of 28

Examples: Graphs of y = loga x, where a > 1

Original location: Ch 3 Examples 26-29 (p.127-136), Ex 3G Q5, 6, 8, 11 (p.138-139) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

Cambridge University Press

Year 11 Exponential functions and logarithms Page 14 of 28

Original location: Ch 3 Examples 26-29 (p.127-136), Ex 3G Q5, 6, 8, 11 (p.138-139) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

Cambridge University Press

Year 11 Exponential functions and logarithms Page 15 of 28

Original location: Ch 3 Examples 26-29 (p.127-136), Ex 3G Q5, 6, 8, 11 (p.138-139) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

Cambridge University Press

Year 11 Exponential functions and logarithms Page 16 of 28

Original location: Ch 3 Examples 26-29 (p.127-136), Ex 3G Q5, 6, 8, 11 (p.138-139) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

Cambridge University Press

Year 11 Exponential functions and logarithms Page 17 of 28

Original location: Ch 3 Examples 26-29 (p.127-136), Ex 3G Q5, 6, 8, 11 (p.138-139) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

Cambridge University Press

Year 11 Exponential functions and logarithms Page 18 of 28

Original location: Ch 3 Examples 26-29 (p.127-136), Ex 3G Q5, 6, 8, 11 (p.138-139) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

Cambridge University Press

Year 11 Exponential functions and logarithms Page 19 of 28

Questions on graphing logarithmic functions using a CAS calculator

Original location: Ch 3 Examples 26-29 (p.127-136), Ex 3G Q5, 6, 8, 11 (p.138-139) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

Cambridge University Press

Year 11 Exponential functions and logarithms Page 20 of 28

Graphing sets of logarithms using a CAS calculator

Original location: Ch 3 (p.136-137) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

Cambridge University Press

Year 11 Exponential functions and logarithms Page 21 of 28

Original location: Ch 3 (p.136-137) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

Cambridge University Press

Year 11 Exponential functions and logarithms Page 22 of 28

Fitting data using a CAS calculator

Original location: Ch 3 Example 31 (p.139-143) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

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Year 11 Exponential functions and logarithms Page 23 of 28

Original location: Ch 3 Example 31 (p.139-143) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

Cambridge University Press

Year 11 Exponential functions and logarithms Page 24 of 28

Example: Graphing data from a table

Original location: Ch 3 Example 31 (p.139-143) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

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Year 11 Exponential functions and logarithms Page 25 of 28

Original location: Ch 3 Example 31 (p.139-143) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

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Year 11 Exponential functions and logarithms Page 26 of 28

Modelling exponential growth using a CAS calculator

Original location: Ch 3 (p.144-145) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

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Year 11 Exponential functions and logarithms Page 27 of 28

Answers

Exponential function questions

Graphing exponentials questions

Original location: Answers (p.576-578) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

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Year 11 Exponential functions and logarithms Page 28 of 28

Graphing logarithms questions

Original location: Answers (p.576-578) © Joe Ousby, Ray Cross, Rick Bowman, Michael Evans, Kay Lipson, Doug Wallace 2008

See www.technologyinmaths.com.au for conditions of use

Cambridge University Press