Copyright © Cengage Learning. All rights reserved. 3 Exponential and Logarithmic Functions.

Slides:



Advertisements
Similar presentations
Exponential and Logarithmic Functions
Advertisements

Exponential and Logarithmic Functions
Copyright © 2011 Pearson, Inc. 3.2 Exponential and Logistic Modeling.
Copyright © Cengage Learning. All rights reserved.
Graphs of Exponential and Logarithmic Functions
Section 5.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models.
Economics 2301 Lecture 8 Logarithms. Base 2 and Base 10 Logarithms Base 2 LogarithmsBase 10 Logarithms Log 2 (0.25)=-2since 2 -2 =1/4Log 10 (0.01)=-2since.
Chapter 3 Linear and Exponential Changes 3
Copyright © Cengage Learning. All rights reserved. 3 Exponential and Logarithmic Functions.
Models of Exponential and Log Functions Properties of Logarithms Solving Exponential and Log Functions Exponential Growth and Decay
5.2 Logarithmic Functions & Their Graphs
3 Exponential and Logarithmic Functions
Exponential and Logarithmic Functions
LOGARITHMS AND EXPONENTIAL MODELS
Exponential and Logarithmic Functions
Copyright © Cengage Learning. All rights reserved. 6 Inverse Functions.
Section 3.5 Exponential and Logarithmic Models. Important Vocabulary Bell-shaped curve The graph of a Gaussian model. Logistic curve A model for describing.
Homework Lesson Handout #5-27 (ODD) Exam ( ): 12/4.
Chapter 3 Exponential and Logarithmic Functions
3 Exponential and Logarithmic Functions
3 Exponential and Logarithmic Functions
Log a x y. Recognize and evaluate logarithmic functions with base a Graph logarithmic functions Recognize, evaluate, and graph natural logarithmic functions.
1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-1 Exponential and Logarithmic Functions Chapter 9.
Copyright © 2010 Pearson Education, Inc. All rights reserved Sec
Session 6 : 9/221 Exponential and Logarithmic Functions.
Copyright © 2010 Pearson Education, Inc. All rights reserved Sec
C2: Exponential Functions Learning Objective: to be able to recognise a function in the form of f(x) = a x.
Chapter 7 Exponential and Logarithmic Functions. 7-1, 7-2, and 7-3 Exponential Growth Exponential Decay The number “e”
Copyright © Cengage Learning. All rights reserved. 1 Functions and Models.
Copyright © 2009 Pearson Education, Inc. CHAPTER 5: Exponential and Logarithmic Functions 5.1 Inverse Functions 5.2 Exponential Functions and Graphs 5.3.
Copyright © Cengage Learning. All rights reserved. 2 Nonlinear Functions and Models.
Exponential and Logistic Functions. Quick Review.
Logs Midterm Review Pre-Calculus. Topic 1: Be able to change logarithmic and exponential forms.
Lesson 3.5 Exponential & Logarithmic Models Homework Deal – Pick one of the following options: 1)Do 30 or so problems a night for the remaining 120 days.
Exponential & Logistic Functions Today you will examine exponential functions and identify and graph exponential and logistic functions.
Section 4.5 Modeling with Exponential & Logarithmic Functions.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 1 Homework, Page 286 Is the function an exponential function? If.
5.2 Logarithmic Functions & Their Graphs Goals— Recognize and evaluate logarithmic functions with base a Graph Logarithmic functions Recognize, evaluate,
Notes Over 8.2 Recognizing Exponential Growth and Decay Exponential Growth Model Exponential Decay Model.
Copyright © Cengage Learning. All rights reserved. 1 Functions and Models.
Section 3.5 Exponential and Logarithmic Models. Compound Interest The compound interest formula: A is the amount in the account after t years. P is the.
Copyright © Cengage Learning. All rights reserved. Exponential and Logarithmic Functions.
Copyright © Cengage Learning. All rights reserved.
Table of Contents Exponential Function - Graphing Example Sketch the graph of the exponential function... Find a few ordered pairs... f(-2) = 3 -2 = 1/9.
MATH III – Exponential and Logarithmic Functions Exponential Growth and Decay.
Exponential Functions Chapter 10, Sections 1 and 6.
Copyright © Cengage Learning. All rights reserved. 3 Exponential and Logarithmic Functions.
CHAPTER 5 REVIEW Exponential and Logarithmic Functions.
INVERSE Logarithmic and Exponential Graphs and Graphing.
Exponential and Logarithmic Functions 4 Copyright © Cengage Learning. All rights reserved.
Logarithmic, Exponential, and Other Transcendental Functions 5 Copyright © Cengage Learning. All rights reserved.
Copyright © 2010 Pearson Education, Inc. All rights reserved Sec
Logarithmic Functions & Their Graphs Goals— Recognize and evaluate logarithmic functions with base a Graph Logarithmic functions Recognize, evaluate, and.
Exponential and Logarithmic Functions
Exponential and Logarithmic Equations
Chapter 6 Section 3.
Logarithmic Functions and Their Graphs
Packet #15 Exponential and Logarithmic Equations
Exponential Functions
Inverse, Exponential and Logarithmic Functions
Exponential Growth and Decay; Logistic Growth and Decay
Section 5.2 – Logarithmic Functions
Exponential and Logarithmic Functions
Inverse, Exponential and Logarithmic Functions
Inverse, Exponential and Logarithmic Functions
Exponential and Logarithmic Functions
Exponential and Logarithmic Functions
Chapter 5.1 How Populations Grow.
Presentation transcript:

Copyright © Cengage Learning. All rights reserved. 3 Exponential and Logarithmic Functions

3.5 EXPONENTIAL AND LOGARITHMIC MODELS Copyright © Cengage Learning. All rights reserved.

3 Recognize the five most common types of models involving exponential and logarithmic functions. Use exponential growth and decay functions to model and solve real-life problems. Use Gaussian functions to model and solve real-life problems. What You Should Learn

4 Use logistic growth functions to model and solve real-life problems. Use logarithmic functions to model and solve real-life problems. What You Should Learn

5 Introduction

6

7 Exponential Growth and Decay

8

9

10

11

12

13

14

15

16

17

18

19 Logistic Growth Models

20 Logistic Growth Models Some populations initially have rapid growth, followed by a declining rate of growth, as indicated by the graph in Figure One model for describing this type of growth pattern is the logistic curve given by the function where y is the population size and x is the time. An example is a bacteria culture that is initially allowed To grow under ideal conditions, and then under less favorable conditions that inhibit growth. A logistic growth curve is also called a sigmoidal curve. Figure 3.40

21

22 Logarithmic Models When a Physical quantity varies over a very large range, it is convenient to take its log to have a more manageable set of numbers.

23

24

25

26

27