The Number e Section 8.3. WHAT YOU WILL LEARN: 1.How to use the number e as the base of exponential...
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![Page 1: The Number e Section 8.3. WHAT YOU WILL LEARN: 1.How to use the number e as the base of exponential functions.](https://reader034.fdocuments.us/reader034/viewer/2022042821/56649f505503460f94c72f48/html5/thumbnails/1.jpg)
The Number e
Section 8.3
![Page 2: The Number e Section 8.3. WHAT YOU WILL LEARN: 1.How to use the number e as the base of exponential functions.](https://reader034.fdocuments.us/reader034/viewer/2022042821/56649f505503460f94c72f48/html5/thumbnails/2.jpg)
WHAT YOU WILL LEARN:
1. How to use the number e as the base of exponential functions.
![Page 3: The Number e Section 8.3. WHAT YOU WILL LEARN: 1.How to use the number e as the base of exponential functions.](https://reader034.fdocuments.us/reader034/viewer/2022042821/56649f505503460f94c72f48/html5/thumbnails/3.jpg)
Oh Boy! Vocabulary
We have many “special” numbers in math. We have pi, i, zero, and we are adding a new one…
The number is called the natural base and we use the letter “e” to represent this number.
This number was discovered by a man named Leonhard Euler
![Page 4: The Number e Section 8.3. WHAT YOU WILL LEARN: 1.How to use the number e as the base of exponential functions.](https://reader034.fdocuments.us/reader034/viewer/2022042821/56649f505503460f94c72f48/html5/thumbnails/4.jpg)
The Value of e
10000
1000
100
10
)10000
11(
)1000
11(
)100
11(
)10
11(
• Evaluate the following on your calculator (use 1.1 for the first number 1.01 for the second, etc):
![Page 5: The Number e Section 8.3. WHAT YOU WILL LEARN: 1.How to use the number e as the base of exponential functions.](https://reader034.fdocuments.us/reader034/viewer/2022042821/56649f505503460f94c72f48/html5/thumbnails/5.jpg)
The Value of e
10000
1000
100
10
)10000
11(
)1000
11(
)100
11(
)10
11(
• Evaluate the following on your calculator (use 1.1 for the first number 1.01 for the second, etc):
597182818284.2e
What number are we “zeroing” in on?
e!
![Page 6: The Number e Section 8.3. WHAT YOU WILL LEARN: 1.How to use the number e as the base of exponential functions.](https://reader034.fdocuments.us/reader034/viewer/2022042821/56649f505503460f94c72f48/html5/thumbnails/6.jpg)
The Rules of e
43 ee
You simplify expressions involving the natural base using the same rules of exponents we used in the previous chapter:
Simplify:
2
3
5
10
e
e 24 )3( xe
![Page 7: The Number e Section 8.3. WHAT YOU WILL LEARN: 1.How to use the number e as the base of exponential functions.](https://reader034.fdocuments.us/reader034/viewer/2022042821/56649f505503460f94c72f48/html5/thumbnails/7.jpg)
You Try
5
8
8
24
e
e
• Simplify.25 )2( xe
![Page 8: The Number e Section 8.3. WHAT YOU WILL LEARN: 1.How to use the number e as the base of exponential functions.](https://reader034.fdocuments.us/reader034/viewer/2022042821/56649f505503460f94c72f48/html5/thumbnails/8.jpg)
Evaluating Natural Base Expression - Calculator
• Evaluate.
e2 e-0.06
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Graphing Natural Base Functions
x-10 -5 5 10
y
-10
-5
5
10
• Graph y = 2e0.75x State the domain and range.
![Page 10: The Number e Section 8.3. WHAT YOU WILL LEARN: 1.How to use the number e as the base of exponential functions.](https://reader034.fdocuments.us/reader034/viewer/2022042821/56649f505503460f94c72f48/html5/thumbnails/10.jpg)
You Try
x-10 -5 5 10
y
-10
-5
5
10
• Graph y = -3e0.5x. State the domain and range.
![Page 11: The Number e Section 8.3. WHAT YOU WILL LEARN: 1.How to use the number e as the base of exponential functions.](https://reader034.fdocuments.us/reader034/viewer/2022042821/56649f505503460f94c72f48/html5/thumbnails/11.jpg)
Another Graphing Example
x-10 -5 5 10
y
-10
-5
5
10
• Graph y = e-0.5(x-2) + 1. State the domain and range.
![Page 12: The Number e Section 8.3. WHAT YOU WILL LEARN: 1.How to use the number e as the base of exponential functions.](https://reader034.fdocuments.us/reader034/viewer/2022042821/56649f505503460f94c72f48/html5/thumbnails/12.jpg)
You Try
x-10 -5 5 10
y
-10
-5
5
10
• Graph y = e0.4(x+1) - 2. State the domain and range.
![Page 13: The Number e Section 8.3. WHAT YOU WILL LEARN: 1.How to use the number e as the base of exponential functions.](https://reader034.fdocuments.us/reader034/viewer/2022042821/56649f505503460f94c72f48/html5/thumbnails/13.jpg)
Compound Interest• When you earn interest on the principal amount
plus the interest already earned, it is called compound interest.
• Formula: A = Pert
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Homework
Homework: page 483, 18-28 even, 34, 36, 50-56 even, 61-66 all, 67, 68, 70, 76