Algebra II Mr. Gilbert

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Algebra IIMr. Gilbert

• Chapter 10.5
• Base e and Natural Logarithms
• Standard Honors

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Agenda

• Warm up
• Work book (participation grade)
• Lesson (calculator required)
• Homework

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Transparency 5
Click the mouse button or press the Space Bar to
display the answers.
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Transparency 5a
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Homework Review
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Communicate Effectively

• e is an irrational number, its formula
• e ? 2.71828
• In a logarithm logea is written ln a
• e is the base and a any real number

• Usage
• To calculate continuous compound interest.
  Aamount, Pprinciple,
• 
  r rate, ttime in years.

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Lesson 5 Contents
This lesson requires a calculator.
Example 1 Evaluate Natural Base Expressions
(2) Example 2 Evaluate Natural Logarithmic
Expressions (2) Example 3 Write Equivalent
Expressions (2) Example 4 Inverse Property of
Base e and Natural Logarithms Example 5 Solve
Base e Equations Example 6 Solve Base e
Inequalities Example 7 Solve Natural Log
Equations and Inequalities
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Example 5-1a
Answer about 1.6487
Answer about 0.0003
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Example 5-1c
Answer 1.3499
Answer 0.1353
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Example 5-2d
Use a calculator to evaluate In 3 to four decimal
places.
Answer about 1.0986
Answer about 0.0003
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Example 5-2f
Answer 0.6931
Answer 0.6931
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Example 5-3a
Answer about 0.0003
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Example 5-3c
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Example 5-4a
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Example 5-4b
Your Turn Evaluate each expression. a. b.
Answer 7
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Example 5-5a
Answer The solution is about 0.3466.
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Example 5-5b
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Example 5-5c
Answer 0.8047
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Example 5-6a
Savings Suppose you deposit 700 into an account
paying 6 annual interest, compounded
continuously. What is the balance after 8 years?
Answer The balance after 8 years would be
1131.25.
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Example 5-6b
How long will it take for the balance in your
account to reach at least 2000?
The balance is at least 2000.
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Example 5-6c
Answer It will take at least 17.5 years for the
balance to reach 2000.
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Example 5-6d
Savings Suppose you deposit 700 into an account
paying 6 annual interest, compounded
continuously. a. What is the balance after 7
years? b. How long will it take for the balance
in your account to reach at least 2500?
Answer 1065.37
Answer at least 21.22 years
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Example 5-7a
Answer The solution is 0.5496. Check this
solution using substitution or graphing.
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Example 5-7b
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Example 5-7c
Answer The solution is all numbers less than
7.5912 and greater than 1.5. Check this
solution using substitution.
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Example 5-7d
Answer about 1.0069
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Homework
See Syllabus 10.5