Unit 4: Exponential & Logarithmic Functions (BI Chapter 6), Day 3: The Natural Base "e"

Learning Objectives:

You will learn the definition and use of the natural base e.
You will be able to graph natural base functions using a graphing calculator.
You will be able to perform operations using the natural base e.
You will be able to use e in application problems, especially in continuous compounding: $LaTeX: A=Pe^{rt}$ .

"Home" Work HW 4.3:

1. Take Notes (yes I will check for these as part of "homework"): Take notes on the introductory video linked here. As the video explains "e" is a number. It is an irrational number like $LaTeX: \sqrt{2}$ or $LaTeX: \pi$ , but it is still just a real number (even though it kind of "looks like" a variable because we use a letter to identify it). It works like any other number, following all the "rules" of mathematics.

For example, the operations are just as you would expect. Write these examples in your notes, also; then try homework:

Addition & subtraction, add (or subtract) the coefficients: or

Multiplication & division; nothing has changed: keep the base the same and follow the exponent rules: $LaTeX: 3e^2\left(2e^3+5e^{13}\right)=6e^5+15e^{15}$

$LaTeX: \left(4e^3\right)^4=4^4\cdot e^{12}=256e^{12}$

$LaTeX: \frac{4e^5}{20e^7}=\frac{1}{5e^2}$

And, , just like any other number!

Be aware:

Working with "e" is just like working with pi -- your answer is more precise if you leave it in terms of "e" rather than using a decimal approximation.
When graphing, remember the value of "e" is between 2 and 3 (about 2.7182818...). Think about what that means about the graph shape (what happens when the value of b > 1?).
Be sure you can find "e" on a graphing or scientific calculator. Notice, too, that Desmos automatically "knows" that when you type "e" you mean the number not a letter.

2. Do the practice in the book: HW #4.3, (Big Ideas 6.2.1): p. 307 #3-15 all; 23-26 all; and 31-34 all.

Optional Notes: 6.2 Introduction to the Natural Base e . You may choose to try these yourself, but this is a preview of next week's work.

General Homework Expectations: Whether you are doing a homework assignment from the BI book, a worksheet, or some other activity, even a Desmos activity, please remember to write all the problems and show your processes in your composition (or note) book. Lists of answers without process will not receive credit!

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Exponential & Logarithmic Functions Unit Resources

Numeracy facts you should master! These basics will continue to be useful as you learn exponential and logarithmic functions.

Squares to 20
Cubes to 10
Powers of 2, up to $LaTeX: 2^{10}=1,024$
Powers of 3, up to
Powers of 10 (Scientific Notation)