1.5 Exponential Functions Monday, August 30, 2004.

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.

Exponential Functions Functions that have the exponent as the variable.

Section 6.2. Example 1: Simplify each Rational Exponent Step 1: Rewrite each radical in exponential form Step 2: Simplify using exponential properties.

CHAPTER Continuity Exponential Growth and Decay Law of Natural Growth(k>0) & (Law of natural decay (k

ACTIVITY 40 Modeling with Exponential (Section 5.5, pp ) and Logarithmic Functions.

Chapter 3 Linear and Exponential Changes 3.2 Exponential growth and decay: Constant percentage rates 1 Learning Objectives: Understand exponential functions.

Differential Equations

Exponential Growth and Decay

Exponential Growth and Decay

Clicker Question 1 The radius of a circle is growing at a constant rate of 2 inches/sec. How fast is the area of the circle growing when the radius is.

4.5 Modeling with Exponential and Logarithmic Functions.

OBJECTIVES: FIND EQUATIONS OF POPULATION THAT OBEY THE LAW OF UNINHIBITED GROWTH AND DECAY USE LOGISTIC MODELS Exponential Growth and Decay; Logistic Models.

Growth and Decay. The Half-Life Time of a Radioactive Elements.

Exponential Growth and Decay Newton’s Law Logistic Growth and Decay

Exponential Growth & Decay By: Kasey Gadow, Sarah Dhein & Emily Seitz.

Exponential/ Logarithmic

8-1: Exponential Growth day 2 Objective CA 12: Students know the laws of fractional exponents, understanding exponential functions, and use these functions.

Functions and Models 1. Exponential Functions 1.5.

6.4 Exponential Growth and Decay Greg Kelly, Hanford High School, Richland, Washington Glacier National Park, Montana Photo by Vickie Kelly, 2004.

1.3 Exponential Functions. Exponential Growth Exponential Decay Applications The Number e …and why Exponential functions model many growth patterns. What.

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

Exponential Growth and Decay 6.4. Exponential Decay Exponential Decay is very similar to Exponential Growth. The only difference in the model is that.

1 SS Solving Exponential Equations MCR3U - Santowski.

Chapter 3 Exponential and Logarithmic Functions

Lesson Rational and Irrational Numbers and Their Properties

Warm Up 1.Quiz: Exponents & Exponential Functions 2.In the Practice Workbook, Practice 8-8 (p. 110) #1, 3, 5.

Exponential Functions Chapter 1.3. The Exponential Function 2.

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

Differentiating exponential functions.

Chapter 3 – Differentiation Rules

Radioactive Half-Lives. perform simple, non-logarithmic half life calculations. graph data from radioactive decay and estimate half life values. graph.

Section 9.2 Exponential Functions  Evaluating Rational & Irrational Exponents  Graphing Exponential Functions f(x) = a x  Equations with x and y Interchanged.

Exponential Functions Section 5.1. Evaluate the exponential functions Find F(-1) Find H(-2) Find Find F(0) – H(1)

Stare at this image…. Do you see the invisible dots?

EXPONENTIAL GROWTH & DECAY; Application In 2000, the population of Africa was 807 million and by 2011 it had grown to 1052 million. Use the exponential.

Differential Equations: Growth and Decay Calculus 5.6.

Lesson – Defining, Rewriting and Evaluating Rational Exponents

10.3: rational exponents April 27, Objectives 1.Define rational exponents 2.Simplify expressions that contain rational exponents 3.Estimate the.

Radioactive Decay A series of reactions that starts with an unstable nucleus and results in a stable nucleus Transmutation- the conversion of one element.

Exponential Modeling Section 3.2a.

Exponential Growth and Decay TS: Making decisions after reflection and review.

Growth and Decay: Integral Exponents

7.4 B – Applying calculus to Exponentials. Big Idea This section does not actually require calculus. You will learn a couple of formulas to model exponential.

12/18/2015 Perkins Honors Precalculus Day 7 Section 4.7.

Growth and Decay Exponential Models.

Chapter 4 Section 4.6 Applications and Models of Exponential Growth and Decay.

6.1 Exponential Growth and Decay

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

By the end of this section, you will be able to: 1. Determine the LCM of polynomials 2. Add and subtract rational expressions Class notes from ___________.

Exponential Growth & Decay Functions Recall from unit 1 that the graph of f(x) = a x (a>1) looks like y = a x As x   then y   but as x  -  then y.

7.3B Applications of Solving Exponential Equations

1.3 Exponential Functions. Slide 1- 2 Exponential Function.

Exponential Functions Chapter 10, Sections 1 and 6.

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

2.4.1 MATHPOWER TM 12, WESTERN EDITION 2.4 Chapter 2 Exponents and Logarithms.

UNIT 7 NUCLEAR REACTIONS 7.3 Calculating Half Life? May 17, 2011 DO NOW: = /4.5 = If we start with 4.5 grams of Radon-222 and over a period.

1 Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 3.1 Exponential Functions Demana, Waits, Foley, Kennedy.

AP Calculus BC Tuesday, 02 February 2016 OBJECTIVE TSW solve exponential growth and decay problems. ASSIGNMENTS DUE FRIDAY –WS Bases Other Than e  given.

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.

Exponential and Logarithmic Functions 4 Copyright © Cengage Learning. All rights reserved.

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

Using Exponential and Logarithmic Functions. Scientists and researchers frequently use alternate forms of the growth and decay formulas that we used earlier.

Exponential Functions You start a new job at age 22. If you invest $125 in a retirement plan each month, your company will invest another $125. The investment.

Honors Precalculus: Do Now Solve for x. 4 2x – 1 = 3 x – 3 You deposit $7550 in an account that pays 7.25% interest compounded continuously. How long will.

Copyright © Cengage Learning. All rights reserved.

Warm-ups: Simplify the following

Chapter 1 Part A Review Sections 1-1 to 1-4.

Presentation transcript:

1.5 Exponential Functions Monday, August 30, 2004

Exponential Functions

Rationals and Irrationals

Laws of Exponents

Applications of Exponents Exponential function occurs very frequently in models of nature and society Examples: population growth, radioactive decay

Radioactive Decay Example The half-life of strontium-90 is 25 years. a. If a sample of strontium-90 has a mass of 24 mg, find an expression for the mass m(t) that remains after t years. b. Find the mass remaining after 40 years. c. Estimate the time required for the mass to be reduced to 5 mg.

The number e

More about e Slope of the tangent line y=2 x m ≈.7 y= 3 x m ≈ 1.1 y=e x m = 1 e ≈

Assignment for Section 1.5 Page 62 – 3, 15, 18,22,26

Hand-In Assignment #1 Due Friday, September 3 Page 23: 20, 24, 26, 40, 52 Page A32: 32, 48, 56, 58, 72 Page 62: 16, 20