Copyright © Cengage Learning. All rights reserved. Pre-Calculus Honors 3.1: Exponential Functions and Their Graphs.

Slides:

Advertisements

Similar presentations

Exponential and Logarithmic Functions

Advertisements

Exponential Functions and Their Graphs Digital Lesson.

Graphs of Exponential and Logarithmic Functions

Exponential and Logarithmic Functions

Exponential Functions and Their Graphs Digital Lesson.

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,

3 Exponential and Logarithmic Functions

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

Exponential Functions. Exponential Functions and Their Graphs.

PRECALCULUS I EXPONENTIAL FUNCTIONS Dr. Claude S. Moore Danville Community College.

Exponential Functions and Their Graphs Digital Lesson.

Exponential Functions

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.

Journal: Write an exponential growth equation using the natural base with a horizontal asymptote of y=-2.

What is the symmetry? f(x)= x 3 –x.

As n gets very large, interest is continuously compounded. Examine the graph of f(n)= (1 + ) n. The function has a horizontal asymptote. As n becomes infinitely.

7.1 Exponential Models Honors Algebra II. Exponential Growth: Graph.

Chapter 11 Section 11.1 – 11.7 Review. Chapter 11.1 – 11.4 Pretest Evaluate each expression 1. (⅔) -4 = ___________2. (27) - ⅔ = __________ 3. (3x 2 y.

Exponential Functions and Their Graphs

Exponential Functions and Their Graphs Digital Lesson.

Exponential Graphs Equations where the variable (x) is the POWER y = ab x – h + k h moves the graph horizontally k moves the graph vertically.

Aim: Continuous Compounding Course: Math Literacy Aim: How does the exponential model fit into our lives? Do Now: An insurance agent wishes to sell you.

1 Example – Graphs of y = a x In the same coordinate plane, sketch the graph of each function by hand. a. f (x) = 2 x b. g (x) = 4 x Solution: The table.

Exponential Functions and Their Graphs Digital Lesson.

Exponential Functions and Their Graphs/ Compound Interest 2015/16.

Section 3.1 Exponential Functions. Definition An exponential function is in the form where and.

Slide Copyright © 2012 Pearson Education, Inc.

Graphing Log Functions Pre-Calculus. Graphing Logarithms Objectives:  Make connections between log functions and exponential functions  Construct a.

Exponential Functions and Their Graphs. 2 Exponential Function Families We’ve already learned about –This is the parent function We’ll expand this to.

3.1 Exponential Functions and Their Graphs The exponential function f with base a is denoted by f(x) = a x and x is any real number.

Chapter 4 Exponential and Logarithmic Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc Exponential Functions.

Lesson 20 – Introducing and Applying Base e. Pre-Calculus 2/22/20161Pre-Calculus.

Warm Up  Complete the Grok Activity on the back of your homework (the one with people at the top)

Copyright © Cengage Learning. All rights reserved. Pre-Calculus Honors 3.4: Solving Exponential and Logarithmic Equations Chapter 3 Test: Tues 12/15 and.

Exponential & Logarithmic functions. Exponential Functions y= a x ; 1 ≠ a > 0,that’s a is a positive fraction or a number greater than 1 Case(1): a >

Math – Exponential Functions

3.1 Exponential Functions and Their Graphs Objectives: Students will recognize and evaluate exponential functions with base a. Students will graph exponential.

MAT150 Unit 4-: Exponential Functions Copyright ©2013 Pearson Education, Inc.

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

Warm Ups Term 4 Week 5. Warm Ups 4/13/15 1.Solve the equation: log x = Find the inverse of the function: f(x) = 2 – x 3.

Algebra II 8-1 (2). Starter: Graph: y = 2(4) x+3 -2 Asymptote: Domain: Range:

3.1 – Exponential Functions and Their Graphs Ch. 3 – Exponential and Logarithmic Functions.

Exponential and Logarithmic Functions

Copyright © Cengage Learning. All rights reserved.

Recall the compound interest formula A = P(1 + )nt, where A is the amount, P is the principal, r is the annual interest, n is the number of times the.

Aim # 4.1 What are Exponential Functions?

Exponential Functions

Chapter 5: Inverse, Exponential, and Logarithmic Functions

Exponential and Logarithmic Functions

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Objective 1A f(x) = 2x + 3 What is the Range of the function

Exponential Functions and Their Graphs

Exponential Functions and Their Graphs

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Chapter 3 Section 1 Exponential Functions and Their Graphs

Section 5.1 – Exponential Functions

4.2 Exponential Functions and Their Graphs

Section 5.2 – Logarithmic Functions

Exponential and Logarithmic Functions

3.1 Exponential Functions and Their Graphs

Exponential Functions and Their Graphs

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Exponential Functions and Their Graphs

Exponential Functions and Their Graphs

Exponential and Logarithmic Functions

Exponential Functions and Their Graphs

Review: How do you find the inverse of a function? Application of what you know… What is the inverse of f(x) = 3x? y = 3x x = 3y y = log3x f-1(x) = log3x.

Packet #13 Exponential and Logarithmic Functions Math 160 Packet #13 Exponential and Logarithmic Functions.

Exponential Functions and Their Graphs

Precalculus Midterm Review

Presentation transcript:

Copyright © Cengage Learning. All rights reserved. Pre-Calculus Honors 3.1: Exponential Functions and Their Graphs

2 Graphs of Exponential Functions y = 0 is a horizontal asymptote (a x  0 as x  ) Domain: (, ) (a –x  0 as x  )Range: (0, ) Continuous

3 The Natural Base e For many applications, the convenient choice for a base is the irrational number e = This number is called the natural base. The function f (x) = e x is called the natural exponential function.

4 Graph f(x) = 3 x. Label asymptote. Determine domain and range.

5 Graph f(x) = 5 – e x. Label asymptote. Determine domain and range.

6 Graph f(x) = 4 x – 2 – 3. Label asymptote. Determine domain and range.

7 Graph f(x) =.5 -(x + 4). Label asymptote. Determine domain and range.

8 Applications Exponential Growth/Decay:

9 Example 8 – Finding the Balance for Compound Interest A total of $9000 is invested at an annual interest rate of 2.5%, compounded quarterly. Find the balance in the account after 5 years.