Intro to Graphing Exponentials Mon Oct 22 nd / Tue Oct 23 rd.

Slides:



Advertisements
Similar presentations
Unit 9. Unit 9: Exponential and Logarithmic Functions and Applications.
Advertisements

Exponential Functions o Work on Exploration 1: Exponential Functions page 22 o Definition of Exponential Function o Graphs of Exponential Growth & Decay.
4.6 (M2) Solve Exponential Equations and Inequalities Performance Exam: Dec. 2 Last Unit Test: Dec. 8 EOCT: Dec. 16 (6 th ), Dec. 17 (7 th ) We will go.
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:
Linear vs. exponential growth Linear vs. exponential growth: t = 0 A = 1x(1+1) 0 = 1 A = 1x0 + 1 = 1.
Intercepts, Exponentials, and Asymptotes Section 3.4 Standard: MCC9-12.F.IF.7a&e Essential Question: How do you graph and analyze exponential functions.
Exponential Growth and Decay
EXAMPLE 4 Classify and write rules for functions SOLUTION The graph represents exponential growth (y = ab x where b > 1). The y- intercept is 10, so a.
8.2 Exponential Decay P Exponential Decay Has the same form as growth functions f(x) = ab x Where a > 0 BUT: 0 < b < 1 (a fraction between 0 & 1)
3.2 Graph Exponential Decay Functions P. 236 What is exponential decay? How can you recognize exponential growth and decay from the equation? What is the.
7.1 Notes: Growth and Decay Functions. What is an exponential function?  The variable is in the exponent rather than the base.  Exponential growth increases.
Exponential Growth and Decay Functions. What is an exponential function? An exponential function has the form: y = ab x Where a is NOT equal to 0 and.
Name: Date: Period: Topic: Adding & Subtracting Polynomials Essential Question : How can you use monomials to form other large expressions? Warm – Up:
How does one Graph an Exponential Equation?
Negative Exponents Fraction Exponent Graphs Exponential function Misc
CHAPTER 1: PREREQUISITES FOR CALCULUS SECTION 1.3: EXPONENTIAL FUNCTIONS AP CALCULUS AB.
5-4 Scientific Notation (p )
Recall: These are equations of the form y=ab x-h +k, ones where the ‘x’ is in the exponent Recall: These are equations of the form y=ab x-h +k, ones where.
8-1 Exploring Exponent Models Objectives:  To identify exponential growth and decay.  To define the asymptote  To graph exponential functions  To find.
Section 7.1: Graph Exponential Growth Functions Chapter 7: Exponential and Logarithmic Functions.
Chapter 1.3 Exponential Functions. Exponential function F(x) = a x The domain of f(x) = a x is (-∞, ∞) The range of f(x) = a x is (0, ∞)
Essential Question: How do you find a growth factor and a decay factor?
Notes Over 8.4 Rewriting Logarithmic Equations Rewrite the equation in exponential form.
Exponential Functions 1. Exponents Review Remember, the following basic exponent rules:
Solving Exponentials By Graphing and Common Base.
Evaluate each expression for the given value of x.
Chapter 8 Test Review Exponents and Exponential Functions
Graphing Exponentials and Logs
Chapter 8 Slide the Eraser. Question 1 write the following using exponents? 7 · 7 2 · 2 · 2 x · x · x· x · x· x · x.
8.1-2 – Exponential Functions. Ex. 1 Sketch the graph of y = 2 x. Then state the functions domain & range.
(7.1 & 7.2) NOTES- Exponential Growth and Decay. Definition: Consider the exponential function: if 0 < a < 1: exponential decay if a > 1: exponential.
State the domain and range of each function Exponential Growth and Decay.
Section 9.2 Exponential Functions  Evaluating Rational & Irrational Exponents  Graphing Exponential Functions f(x) = a x  Equations with x and y Interchanged.
8-2: Exponential Decay Objective Ca Standard 12: Students know the laws of fractional exponents, understand exponential functions and use these functions.
Exponential Functions. An exponential function is a function where the variable is an exponent. Examples: f(x) = 3 x g(x) = 5000(1.02) x h(x) = (¾) x+2.
Multiplication of Exponents
7.4 – Roots of Real Numbers. Real vs. Imaginary Roots – opposite of exponents!
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.
Multiplication of Exponents Notes
10.3: rational exponents April 27, Objectives 1.Define rational exponents 2.Simplify expressions that contain rational exponents 3.Estimate the.
Power Value Zero and Negative Exponents.
$100 $200 $300 $400 $500 $200 $300 $400 $500 Exponents Scientific Notation Exponential Growth and Decay Properties of exponents Geometry Sequences.
Growth and Decay: Integral Exponents
Today in Precalculus Notes: Intro to Exponential Functions (no handout) Homework.
Notes Over 8.2 Recognizing Exponential Growth and Decay Exponential Growth Model Exponential Decay Model.
4.4 Graph Exponential Growth Functions
Example Divide 2y 2 – 6y + 4g – 8 by 2. 2y 2 – 6y + 4g y 2 – 6y + 4g Simply divide each term by 2 y 2 – 3y + 2g - 4.
Holt McDougal Algebra 2 Exponential Functions, Growth, and Decay Exponential Functions, Growth and Decay Holt Algebra 2Holt McDougal Algebra 2 How do.
Exponents Mr. Platt. What is an exponent? An An exponent tells how many times a number called the base is used as a factor. 3 4 Base Exponent.
Exploring Exponential Functions Using a Graphing Calculator.
Graphing Exponential Growth and Decay. An exponential function has the form b is a positive number other than 1. If b is greater than 1 Is called an exponential.
8-1: Exponential Growth Objective CA 12: Students know the laws of fractional exponents, understanding exponential functions, and use these functions in.
8.5 and 8.6 Writing and Graphing Exponential Growth and Decay Functions Students will learn to Write exponential growth and decay functions Graph exponential.
Thurs 2/4 Lesson 7 – 1 Learning Objective: To graph exponential functions & solve interest problems Hw: Pg. 439 #10-25 all.
Multiplying Monomials. Monomial – Any number, or variable, or product /quotient of numbers and variables. Ex: 6x 6x - x 2 y 2 - y 2 z 3 ½xy In an expression,
Exponential Growth Exponential Decay Example 1 Graph the exponential function given by Solution xy or f(x) 0 1 –1 2 – /3 9 1/9 27.
Fri 2/5 Lesson 7 – 1 Learning Objective: To graph exponential functions & solve interest problems Hw: Pg. 439 #10, 14, 17 – 22, 26 – 29, CC#45.
What are the four different types of functions we have learned about?
8-2: Exponential Decay Day 2 Objective Ca Standard 12: Students know the laws of fractional exponents, understand exponential functions and use these functions.
Exponential Functions 4.3 **You might want graph paper**
8.1 & 8.2 Exponential Functions 3/10/2014. In this lesson we will learn … What an exponential function is. Difference between exponential growth and decay.
10.5 Properties of Logarithms. Remember…
Calculus Sections 5.1 Apply exponential functions An exponential function takes the form y = a∙b x where b is the base and b>0 and b≠1. Identify as exponential.
Objectives: The student will be able to… 1)Graph exponential functions. 2)Solve exponential equations and inequalities.
8.1 & 8.2 Exponential Growth and Decay 4/16/2012.
Exponent Rules: Continued
Lesson 8.1 How do you use properties of exponents involving products?
Module 10: Lesson 10.2 Graphing Exponential Functions
L2-5 Objective: Students will solve and graph equations and inequalities involving absolute values Absolute Value Function Parent Function.
Presentation transcript:

Intro to Graphing Exponentials Mon Oct 22 nd / Tue Oct 23 rd

Remember Exponent Rules…

Vocabulary Exponential Function – has the form y = ab x, where a ≠ 0 and the base b is a positive number other than 1. If a > 0 and b > 1, then the function y = ab x is an Exponential Growth Function, and b is called the Growth Factor Exponential Decay Function – has the form y = ab x, where a > 0 and 0 < b < 1 (this means b is a fraction)

Ex 1) Growth

Ex 2) Decay

Ex 3)

Ex 4)

Growth vs Decay

Ex 5)

Try these 6) 7) 8)

Ex 6) XY

Ex 7) XY

Ex 8) XY

Graphing y = ab x-h +k h – moves graph left and right (opposite) k – moves graph up and down