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, ∞)

Slides:

Advertisements

Similar presentations

Exponential Functions Functions that have the exponent as the variable.

Advertisements

Exponential and Logistic Modeling

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

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:

Exponential and Logarithmic Functions

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.

Objective: Students will be able to write and evaluate exponential expressions to model growth and decay situations.

Partner practice Chapter 8 Review WHITEBOA RD. Chapter 8 Review DRAW -The basic shape of the graph of a linear equation -The basic shape of the graph.

4-1 exponential functions, growth and decay

CHAPTER 1: PREREQUISITES FOR CALCULUS SECTION 1.3: EXPONENTIAL FUNCTIONS AP CALCULUS AB.

Exponential Functions. Exponential Function f(x) = a x for any positive number a other than one.

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,

Pg. 259/245/68 HW Review Pg. 255#6, 14, 24, 28, 35, 51 Pg. 268#1, 3, 5 – 9 odd, 15 #58#59 ft/sec #60#61t = sec #62 V(t) = 36πt 3 #63V(5) = 14,

Exponential Growth Exponential Decay Graph the exponential function given by Example Graph the exponential function given by Solution x y, or f(x)

8-1 Exploring Exponent Models Objectives:  To identify exponential growth and decay.  To define the asymptote  To graph exponential functions  To find.

6.1 Exponential Growth and Decay

Section 4.1 Exponential Functions

Section 7.1: Graph Exponential Growth Functions Chapter 7: Exponential and Logarithmic Functions.

Exponential Functions Chapter 1.3. The Exponential Function 2.

Essential Question: How do you find a growth factor and a decay factor?

Exponential Functions Section 1.3. Exponential Functions f(x) = a x Example: y 1 = 2 x y 2 = 3 x y 3 = 5 x For what values of x is 2 x

Exponential Functions

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

Evaluate each expression for the given value of x.

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

Graphing Exponentials and Logs

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

Objective: TSW graph exponential functions and identify the domain and range of the function.

State the domain and range of each function Exponential Growth and Decay.

Chapter 7 Exponential and Logarithmic Functions. 7-1, 7-2, and 7-3 Exponential Growth Exponential Decay The number “e”

Exponential and Logistic Functions. Quick Review.

Exponential Functions and Their Graphs

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

Real Exponents Chapter 11 Section 1. 2 of 19 Pre-Calculus Chapter 11 Sections 1 & 2 Scientific Notation A number is in scientific notation when it is.

Chapter 1.5 Functions and Logarithms. One-to-One Function A function f(x) is one-to-one on a domain D (x-axis) if f(a) ≠ f(b) whenever a≠b Use the Horizontal.

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.

Review of Chapter 8. Graphing Exponential Functions: Make and table and graph the function for the domain {0, 1, 2, 3} Plug in 0, 1, 2, and 3 in for x.

Functions & Graphs (1.2) What is a function? Review Domain & Range Boundedness Open & Closed Intervals Distance from a point to a line.

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.

Xy What is the Domain? What is the Range?. xy What is the Domain? What is the Range?

7.1 E XPONENTIAL F UNCTIONS, G ROWTH, AND D ECAY Warm Up Evaluate (1.08) (1 – 0.02) ( ) –10 ≈ ≈ ≈ Write.

Holt McDougal Algebra 2 Exponential Functions, Growth, and Decay Exponential Functions, Growth and Decay Holt Algebra 2Holt McDougal Algebra 2 How do.

Exponential Functions Exponential Growth Exponential Decay y x.

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

Warm Up Evaluate (1.08) (0.95) (1 – 0.02) ( ) –10 ≈ ≈ ≈ ≈

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.

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.

Exponential Functions Chapter 10, Sections 1 and 6.

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.

7-1 Exponential Functions

Objective: Students will be able to write equivalent forms for exponential and logarithmic functions, and can write, evaluate, and graph logarithmic functions.

6.2 Exponential Functions Objective: Classify an exponential function as representing exponential growth or exponential decay. Calculate the growth of.

Exponential Equations and LOG’s f(x) = y = a x Log a {y} = x Log 10 {y} / Log 10 {a} = x.

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

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.

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

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

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.

6.1 Exponential Functions

1.3 Exponential Functions Day 1

Exponential and Logistic Modeling

Algebra I Chapter 8 Review

Lesson 1.3: Exponential Functions

1.7 Represent Graphs as Functions

Functions PreCalculus 1-2.

(4)² 16 3(5) – 2 = 13 3(4) – (1)² 12 – ● (3) – 2 9 – 2 = 7

4.3 Use Functions Involving e

Presentation transcript:

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, ∞)

Graphing an Exponential Function Graph the function y = 2(3 x ) – 4 State the domain and range Domain is (-∞, ∞) Range is (-4, ∞)

Rules for Exponents If a > 0 and b > 0, the following hold for all real numbers x and y. 1) a x  a y = a x+y 2) a x /a y = a x-y 3) (a x ) y = a xy 4) a x  b x = (ab) x 5) (a/b) x = a x /b x 6) a -1 = 1/a

Exponential Regression Use the following table to predict the US population in the year 2020 Find an exponential equation to fit the data Find the population in 2070 yearpopulation

Exponential growth vs Exponential Decay A substance decrease is mass over time such as radioactive decay The function y = k  a x is exponential growth is a > 1 The function y = k  a x is exponential decay is 1 > a > 0

The Number e Known as the natural number e = Banks use compounded continuously y = P  e rt P = initial investment, r = rate, t = time(years), y = investment after t years Find y where p = $10,000, r = 5%, t = 25 years

Homework Pg 26 #1-5 Quick Review Pg 26 # 1-21 odd