Name ________________________________________ Date __________________ Class__________________
Reading Strategies
LESSON
4-6
Use a Graphic Organizer
Definition
Facts
The number e is an irrational constant
like π. You can estimate e by using very
large values of n in the formula.
A logarithm with base e is called a
natural logarithm (ln x).
1⎞
⎛
f (n ) = ⎜ 1 + ⎟
n⎠
⎝
n
The functions ex and ln x have the same
properties as the other exponential and
logarithmic functions you have studied.
≈ 2.7182818…
e ≈ 2.7182818…
Example (compound interest)
Useful Hints
For a principal investment of $100
with a growth rate of 5% for 10 years
compounded continuously, the total
amount will be:
You can use the property of inverse
functions to solve many problems
containing e and ln.
A = Pe
rt
0.05 × 10
= 100 • e
For example:
ln e 3 = 3 and e ln 3 = 3
= $164.87
Answer each question.
1. a. Rewrite e 3ln x using the Power Property of logarithms.
b. Now simplify.
2. The graph shows g(x) = ex and g–1(x) = ln x.
a. Label each curve with the correct function.
b. What transformation is represented by the
2 curves?
______________________________________
c. Explain how you can tell that they are inverse
functions.
_____________________________________________
3. A = Pert is a formula used for continuously compounded interest.
a. Which variable represents the principal or starting amount?
b. Which variable represents the time length of the investment?
c. Which variable represents the rate of interest paid on the investment?
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
4-50
Holt McDougal Algebra 2
Year
2006
2007
2008
2009
2010
t
3
4
5
6
7
Population,
Pt
257
282
309
340
373
4. C
5. C
6. C
7. D
b.
Reading Strategies
1. a. e3 ln x = eln x
3
c. y = 0
d. Translated 1 unit left
b. x3
2. y = 0; reflected across the x-axis
2. a.
b. Reflection over the line y = x
3. y = 0; horizontal stretch by factor of 2
c. Possible answer: The x- and yvalues of each point in one graph
are reversed in the other graph.
3. a. P
b. t
c. r
4-7 TRANSFORMING EXPONENTIAL
AND LOGARITHMIC FUNCTIONS
Practice A
1. a.
x
f(x)
−3
0.0625
5. g(x) = 82x
4. g(x) = ln (−x)
−2
0.25
−1
1
0
4
6. g(x) = 4(3x)
1
16
7. a. g(x) = log(x + 3)
b. g(x) = −log(x + 3)
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A49
Holt McDougal Algebra 2