Title: Algebra II Mr. Gilbert
1Algebra IIMr. Gilbert
- Chapter 10.5
- Base e and Natural Logarithms
- Standard Honors
2Agenda
- Warm up
- Work book (participation grade)
- Lesson (calculator required)
- Homework
3Transparency 5
Click the mouse button or press the Space Bar to
display the answers.
4Transparency 5a
5Homework Review
6Communicate 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. -
7Lesson 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
8Example 5-1a
Answer about 1.6487
Answer about 0.0003
9Example 5-1c
Answer 1.3499
Answer 0.1353
10Example 5-2d
Use a calculator to evaluate In 3 to four decimal
places.
Answer about 1.0986
Answer about 0.0003
11Example 5-2f
Answer 0.6931
Answer 0.6931
12Example 5-3a
Answer about 0.0003
13Example 5-3c
14Example 5-4a
15Example 5-4b
Your Turn Evaluate each expression. a. b.
Answer 7
16Example 5-5a
Answer The solution is about 0.3466.
17Example 5-5b
18Example 5-5c
Answer 0.8047
19Example 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.
20Example 5-6b
How long will it take for the balance in your
account to reach at least 2000?
The balance is at least 2000.
21Example 5-6c
Answer It will take at least 17.5 years for the
balance to reach 2000.
22Example 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
23Example 5-7a
Answer The solution is 0.5496. Check this
solution using substitution or graphing.
24Example 5-7b
25Example 5-7c
Answer The solution is all numbers less than
7.5912 and greater than 1.5. Check this
solution using substitution.
26Example 5-7d
Answer about 1.0069
27Homework
See Syllabus 10.5