9.3 - The Natural Base, e Lesson Slides: 9 Slides

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?"

1

You-ler

2

Oil-er

3

Ee-ler

4

Multiple Select

Select all of the alternative names for the number "e"

1

Natural Number

2

Euler's Number

3

Natural Base

4

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.

1

True

2

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

$e^3\cdot e^6$

$\frac{16e^5}{4e^4}$

\left(3e^{4x}\right)^2

11

Multiple Choice

Simplify.

e^{-4}\cdot e^{-5}

1

$e^9$

2

$e^{-9}$

3

$e^{-45}$

4

$e^{45}$

12

Multiple Choice

Simplify.

\frac{30e^5}{4e^2}

1

$\frac{30e^3}{4}$

2

$\frac{15e^7}{2}$

3

$\frac{15e^{10}}{2}$

4

$\frac{15e^3}{2}$

13

Multiple Choice

Simplify.

\left(2e^{-3}\right)^3

1

$6e^{-9}$

2

$8e^{-9}$

3

$6e^{-6}$

4

$8e^9$

14

15

Multiple Choice

If k is positive in e^kx, what happens as x increases?

1

exponential growth

2

decay

3

grows in the negative direction

4

stays constant

16

Multiple Choice

If k is negative in e^kx, what happens as x increases?

1

Growth

2

Slow growth

3

decays towards zero

4

stays constant

5

Gets large and negative

17

Multiple Choice

If k is fractional in e^kx, what happens as x increases?

1

grows rapidly

2

grows slowly

3

decays towards zero

4

stays constant

18

What is the rate of increase or decrease?

$y=2e^{-2x}$

19

Fill in the Blanks

What is the rate of increase or decrease? Round to the nearest tenth (one decimal place) and write as a percent.

y=e^{-0.5x}

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