4­6 The Natural Base, e­ period 1.notebook
February 03, 2015
Bellwork 2-3-15
Simplify.
1. log2810,000
2. log44x –1
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4­6 The Natural Base, e­ period 1.notebook
February 03, 2015
The domain of f(x) = ln x is {x|x > 0}.
The range of f(x) = ln x is all real numbers.
All of the properties of
logarithms also apply to
natural logarithms.
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4­6 The Natural Base, e­ period 1.notebook
February 03, 2015
Example 2: Simplifying Expression with e or ln
Simplify.
A. ln e0.15t
B. e3ln(x
+1)
C. ln e2x + ln ex
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4­6 The Natural Base, e­ period 1.notebook
February 03, 2015
Check It Out! Example 2
Simplify.
a. ln e3.2
c. ln ex
b. e2lnx
+4y
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4­6 The Natural Base, e­ period 1.notebook
February 03, 2015
The formula for continuously compounded interest is A = Pert,
where A is the total amount, P is the principal, r is the annual
interest rate, and t is the time in years.
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4­6 The Natural Base, e­ period 1.notebook
February 03, 2015
Example 3: Economics Application
What is the total amount for an investment of $500 invested
at 5.25% for 40 years and compounded continuously?
A = Pert
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4­6 The Natural Base, e­ period 1.notebook
February 03, 2015
Check It Out! Example 3
What is the total amount for an investment of $100 invested
at 3.5% for 8 years and compounded continuously?
A = Pert
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4­6 The Natural Base, e­ period 1.notebook
February 03, 2015
Lesson Quiz
Simplify.
1. ln e–10t
2. e0.25 lnt
3. –ln ex
4. 2ln ex2
5. What is the total amount for an investment of $1000 invested at
7.25% for 15 years and compounded continuously?
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4­6 The Natural Base, e­ period 1.notebook
February 03, 2015
Homework: Complete Worksheet Practice A
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