Exponential Functions

Slides:

Advertisements

Similar presentations

8-6 Compound Interest and Exponential Growth

Advertisements

Exponential Functions Functions that have the exponent as the variable.

7-6 & 7-7 Exponential Functions

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

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

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

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 1- 1.

Section 6.4 Solving Logarithmic and Exponential Equations

7.2 Compound Interest and Exponential Growth ©2001 by R. Villar All Rights Reserved.

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, ∞)

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

Sect 8.1 To model exponential growth and decay Section 8.2 To use e as a base and to apply the continuously and compounded interest formulas.

Applications of Logs and Exponentials Section 3-4.

Exponential and Logistic Functions. Quick Review.

Exponential Growth & Decay

The Number e Section 8.3. WHAT YOU WILL LEARN: 1.How to use the number e as the base of exponential functions.

Section 6 Chapter Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives Exponential and Logarithmic Equations; Further Applications.

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

8.3 Applications of Exponential Functions 3/12/2014.

Exponential Growth and Decay 6.4. Slide 6- 2 Quick Review.

1.3 Exponential Functions. Slide 1- 2 Exponential Function.

ACTIVITY 39 Exponential and Logarithmic (Section 5.4, pp ) Equations.

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.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 1- 1.

Copyright © Cengage Learning. All rights reserved.

Chapter 5: Inverse, Exponential, and Logarithmic Functions

Exponential Functions

8-8 Exponential Growth and Decay

Exponential Growth and Decay

Exponential Functions

1.3 Exponential Functions Day 1

Interpreting Exponential Functions

Chapter 5: Inverse, Exponential, and Logarithmic Functions

Exponential and Logarithmic Functions

Algebra I Chapter 8 Review

AP Calculus AB Day 4 Section 6.2 9/14/2018 Perkins.

Module 12-3 Objective Solve problems involving exponential growth and decay.

6.1 Exponential Growth and Decay Functions

Lesson 1.3: Exponential Functions

6.4 Exponential Growth and Decay, p. 350

Rules for Differentiation

Rules for Differentiation

What do all of these have to do with Calculus?!?!?

7.4 Exponential Growth and Decay

Warm Up Simplify each expression. 1. ( )2 3.

Exponential Growth and Decay

Exponential Equations Applications.

Exponential Growth and Decay

Connecting f′ and f″ with the graph of f

Exponential Functions

Definite Integrals and Antiderivatives

Exponential Growth and Decay

Connecting f′ and f″ with the graph of f

Exponential Systems.

Rules for Differentiation

Exponential and Logarithmic Functions

Warm-Up Evaluate log x for each value. x = 10 x = 0.1 x = -10 x = 1

Derivatives of Exponential and Logarithmic Functions

Functions and Logarithms

Exponential Growth & Decay

Definite Integrals & Antiderivatives

6.1 Exponential Growth and Decay Functions

Derivatives of Exponential and Logarithmic Functions

4.3 Use Functions Involving e

Compounded and Continuous Interest

Jeopardy Choose a category. Click to begin..

Exponential Growth and Decay

Presentation transcript:

Exponential Functions Chapter 1 Prerequisites for Calculus Section 1.3 Exponential Functions

Quick Review

Quick Review

Quick Review

Quick Review

Quick Review

Quick Review

Quick Review Solutions

Quick Review Solutions

What you’ll learn about Exponential functions Rules of exponents Applications of exponential functions (growth and decay) Compound interest The number e …and why Exponential functions model many growth patterns.

Exponential Function

Exponential Growth

Exponential Growth

Rules for Exponents

Half-life Exponential functions can also model phenomena that produce decrease over time, such as happens with radioactive decay. The half-life of a radioactive substance is the amount of time it takes for half of the substance to change from its original radioactive state to a non-radioactive state by emitting energy in the form of radiation.

Exponential Growth and Exponential Decay

Example Finding Zeros

Compound Interest Formula If an account begins with principal P and earns an annual interest rate r compounded n times per year, then the value of the account in t years is

The Number e

The Number e

Example The Number e

Example The Number e

Continuously Compounded Interest Formula If an account begins with principal P and earns an annual interest rate r compounded continuously, then the value of the account in t years is

Quick Quiz Sections 1.1 – 1.3

Quick Quiz Sections 1.1 – 1.3

Quick Quiz Sections 1.1 – 1.3

Quick Quiz Sections 1.1 – 1.3

Quick Quiz Sections 1.1 – 1.3

Quick Quiz Sections 1.1 – 1.3