Objectives: 1. Be able to find the Euler Number. 2.Be simplify expressions using the Natural base (with a calculator also) 3.Be able to graph a Natural.

Slides:

Advertisements

Similar presentations

State the domain and range of each function. 3.1 Graphs of Exponential Functions.

Advertisements

Bellwork 1.How much money would you need to deposit on your 20 th birthday if you want to end with $8250 on your 30 th birthday and your interest rate.

Objectives: 1.Be able to graph the exponential growth parent function. 2.Be able to graph all forms of the exponential growth function Critical Vocabulary:

A Dash of Limits. Objectives Students will be able to Calculate a limit using a table and a calculator Calculate a limit requiring algebraic manipulation.

4_1 Day 2 The natural base: e.. WARM-UP: Graph (5/3)^x (5/3)^-x -(5/3)^x (5/3) ^x (5/3)^(x-2)

Exponential and Logarithmic Functions

Exponential Functions and their Graphs

Graph 8 a. Graph b. Domain _________ c. Range __________

1.) If there are initially 100 fruit flies in a sample, and the number of fruit flies decreases by one-half each hour, How many fruit flies will be present.

Exponential functions have a variable in the Exponent and a numerical base. Ex. Not to be confused with power functions which Have a variable base. Ex.

8.3 The number e p. 480 What is the Euler number? How is it defined? Do laws of exponents apply to “e” number? How do you use “e” on your calculator? When.

1. Given the function f(x) = 3e x :  a. Fill in the following table of values:  b. Sketch the graph of the function.  c. Describe its domain, range,

Section 6.3 Compound Interest and Continuous Growth.

Exponential Functions. Exponential Functions and Their Graphs.

Section 4.1 Exponential Functions

Exponential Functions Section 3.1. What are Exponential Functions?

4.3 Use Functions Involving e p. 244 What is the Euler number? How is it defined? Do laws of exponents apply to “e” number? How do you use “e” on your.

Notes Over 8.4 Rewriting Logarithmic Equations Rewrite the equation in exponential form.

Graph Horizontal Asymptote: y = -1 Domain: Range:y > -1 all real numbers a = ____ 2 b= ____ 3 h = ____ 2 k = ____.

6.6 The Natural Base, e Objectives: Evaluate natural exponential and

8.1-2 – Exponential Functions. Ex. 1 Sketch the graph of y = 2 x. Then state the functions domain & range.

7.1 Exponential Models Honors Algebra II. Exponential Growth: Graph.

THE NATURAL BASE EXAMPLE 1 Simplify natural base expressions Simplify the expression. a.e2e2 e5e5 = e = e7e7 b. 12e4e4 3e3e3 = e 4 – 3 4 = 4e4e.

Exponential Functions and Their Graphs

Exponential Functions and Their Graphs Digital Lesson.

8-2: Exponential Decay Objective Ca Standard 12: Students know the laws of fractional exponents, understand exponential functions and use these functions.

Algebra II w/ trig. Exponential Functions – has the form y= ab x, where a ≠0, b>0, and b≠1 - y represents the quantity after time is expired - a represents.

Exponential Graphs Equations where the variable (x) is the POWER y = ab x – h + k h moves the graph horizontally k moves the graph vertically.

Change & Evaluate the following Logarithmic Equations to Exponential Equations.

Algebra II Honors January 5 th Students will complete daily warm-up problems. Students will be able to model exponential growth and decay. Students will.

Applications of Exponential Functions

6.6 The Natural Base, e Warm-up Learning Objective: To evaluate natural exponential and natural logarithmic functions and to model exponential growth and.

9x – 7i > 3(3x – 7u) 9x – 7i > 9x – 21u – 7i > – 21u

Notes Over 8.2 Recognizing Exponential Growth and Decay Exponential Growth Model Exponential Decay Model.

Logarithmic Functions

Section 3.1 Exponential Functions. Definition An exponential function is in the form where and.

Students will be able to: Use multiplication properties of exponents to evaluate and simplify expressions. Objective 8.1.

EXPONENTIAL FUNCTIONS Section TOPIC FOCUS I can… Identify exponential growth and decay Graph exponential functions.

Exponential Functions Exponential Growth Exponential Decay y x.

3.1 Exponential Functions and Their Graphs The exponential function f with base a is denoted by f(x) = a x and x is any real number.

8-1: Exponential Growth Objective CA 12: Students know the laws of fractional exponents, understanding exponential functions, and use these functions in.

Lesson 20 – Introducing and Applying Base e. Pre-Calculus 2/22/20161Pre-Calculus.

Exponential Functions 4.3 **You might want graph paper**

Exponential Growth and Decay. M & M Lab Part 1- Growth What happened to the number of M&Ms? Part 2-Decay What happened to the number of M&Ms? Increased.

4.3 Use Functions Involving e PROJECT DUE: Tomorrow Quiz: Tomorrow Performance Exam: Friday *We will be having a book check tomorrow…. BRING BOTH.

Unit 8, Lesson 2 Exponential Functions: Compound Interest.

6.2 Exponential Functions Notes Linear, Quadratic, or Exponential? Exponential Growth or Decay? Match Graphs Calculate compound Interest.

8.2 Interest Equations Key Q-How is an exponential function used to find interest? These are all money problems so you should have two decimal places.

Section Vocabulary: Exponential function- In general, an equation of the form, where, b>0, and, is known as an exponential function. Exponential.

8-3: The Number ‘e’ (Day 1) Objective (Ca. Standard 12): Students know the laws of fractional exponents, understand exponential function, and use these.

3.1 Exponential Functions and Their Graphs Objectives: Students will recognize and evaluate exponential functions with base a. Students will graph exponential.

Graphs of Exponential Functions. Exponential Function Where base (b), b > 0, b  1, and x is any real number.

Bellwork Evaluate each expression Solve. for x = bacteria that double 1. every 30 minutes. Find the 2. number of bacteriaafter 3 hours

Objectives: The student will be able to… 1)Graph exponential functions. 2)Solve exponential equations and inequalities.

Warm Up Simplify. x 3w z x – 1 1. log10x 2. logbb3w 3. 10log z

Obj: Evaluate and graph exponential functions. Use compound formulas. Warm up 1.Find the limit. x ,00050,000100,000150,000 y.

1. An account with a balance of $1000 pays 3. 65% annual

Simplify the expression.

The Natural Base, e Essential Questions

(10 ) WARM UP Simplify the expression. 1. e –4x e12x ANSWER

Lesson 6.2 The Natural Base e

7.3 Use Functions Involving e

Objective 1A f(x) = 2x + 3 What is the Range of the function

7.3 Use Functions Involving e

Notes Over 8.3 Simplifying Natural Base Expressions

6.3 Logarithms and Logarithmic Functions

Lesson 1.4 Page 25 Ordered Pairs and Relations.

8.3 The Number e.

Exponential Functions and Their Graphs

Exponential Functions and Their Graphs

Presentation transcript:

Objectives: 1. Be able to find the Euler Number. 2.Be simplify expressions using the Natural base (with a calculator also) 3.Be able to graph a Natural Base Exponential. Objectives: Euler Number, Natural base

Value of “n”FormulaValueSignificance Annually Semi-Annually Quarterly Monthly Daily Hourly Minutely 31,536, , , Secondly Use the expression to fill in the table: I. The Euler Number

II. The Natural Base The Natural Base e: The natural base e is irrational. It is defined as follows: As n approaches ∞ approaches e ≈ Directions: Simplify the natural base expressions 1. e 2 e 5 e 2+5 e7e7 2. 4e 4-3 4e 3. (5e -3x ) e -6x Directions: Evaluate each expression with a calculator 1. e e 3/

III. Graphing a Natural Base Exponential Function Form: f(x) = ae rx If a > 0 and r > 0, then the function is an exponential growth If a > 0 and r < 0, then the function is an exponential decay

Graph: f(x) = 3e.25x Exponential Growth x f(x) Domain: All Real Numbers Range: y > 0 III. Graphing a Natural Base Exponential Function

Graph: f(x) = e.-0.75(x - 2) + 1 Exponential Decay x f(x) Domain: All Real Numbers Range: y > 1 III. Graphing a Natural Base Exponential Function

Page #3-49 odd (24 problems) DOMAIN AND RANGE ON ALL GRAPHS!!!!!

Use the expression to fill in the table: I. The Euler Number Value of “n”FormulaValueSignificance 31,536, , ,600