
Natural Base E Lesson
Presentation
•
Mathematics
•
11th - 12th Grade
•
Hard
Joseph Anderson
Used 1+ times
FREE Resource
9 Slides • 10 Questions
1
9.3 - The Natural Base, e
2
Leonhard Euler (1707-1783)
Swiss mathematician responsible for the development of a new number "e"
This number would be called the "natural base" or "Euler's number"
Applications include compound interest in finance.
3
Multiple Choice
How do you pronounce "Euler?"
You-ler
Oil-er
Ee-ler
4
Multiple Select
Select all of the alternative names for the number "e"
Natural Number
Euler's Number
Natural Base
Euler's Base
5
Pi vs. Natural Base
Both irrational numbers.
Pi is the ratio between a circle's circumference and its diameter.
e is base rate of growth shared by all continually growing processes
6
Multiple Choice
Applications of "e" include financial calculations with continuously compounded interest.
True
False
7
One way of approximating the value of "e"
8
Another way of approximating the value of e.
9
10
Simplifying Natural Base Expressions
e3⋅e6
4e416e5
(3e4x)2
11
Multiple Choice
Simplify.
e−4⋅e−5e9
e−9
e−45
e45
12
Multiple Choice
Simplify.
4e230e5430e3
215e7
215e10
215e3
13
Multiple Choice
Simplify.
6e−9
8e−9
6e−6
8e9
14
15
Multiple Choice
If k is positive in ekx, what happens as x increases?
exponential growth
decay
grows in the negative direction
stays constant
16
Multiple Choice
If k is negative in ekx, what happens as x increases?
Growth
Slow growth
decays towards zero
stays constant
Gets large and negative
17
Multiple Choice
If k is fractional in ekx, what happens as x increases?
grows rapidly
grows slowly
decays towards zero
stays constant
18
What is the rate of increase or decrease?
y=2e−2x
19
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