Do Now Rhonda hears a rumor at 8:00 A.M. She immediately tells her two best friends the rumor. One hour later Rhonda’s friends have each told two of their.

Slides:

Advertisements

Similar presentations

Section 12.2 Exponential Functions. EXAMPLE Solution Graph ƒ (x) = 2 x.

Advertisements

Exponential Functions

Warm-Up 1) A town with a current population of 701,500 has a growth rate of 1.4 percent. Find the multiplier for the rate of exponential growth. 5 minutes.

4.1 Graph Exponential GrowthFunctions p. 228 What is an exponential function? What is exponential growth function? What is an asymptote? What information.

EXAMPLE 5 Find the balance in an account You deposit $4000 in an account that pays 2.92% annual interest. Find the balance after 1 year if the interest.

7.7 Day 1 Notes Base e and Natural Logarithms

7.1 Exponential Growth p. 478 What you should learn: Goal 1

Graph Exponential Growth Functions

8.1 Exponential Growth. Learning Targets Students should be able to…  Graph exponential growth functions.

4.1 Exponential Growth Functions Retesting Opportunity: Dec Quiz: Dec. 3 Performance Exam: Dec. 4.

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

(3 s -5 t 3 s 2 ) 2 1.x 0 =1 2.x a x b = x a+b 3.x a = x a-b xbxb 4.(x a ) b = x ab 5.x -a = 1/x a 6.x a/b = ( b √x) a.

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)

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

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

Exponential Functions Section 3.1. What are Exponential Functions?

Name:__________ warm-up 7-2 State the domain and range of y = –3(2) x State the domain and range of.

Splash Screen. Lesson Menu Five-Minute Check (over Chapter 2) Then/Now New Vocabulary Key Concept:ExponentialKey Concept:Exponential FunctionFunction.

2 pt 3 pt 4 pt 5pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2pt 3 pt 4pt 5 pt 1pt 2pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4pt 5 pt 1pt Evaluate Separate the log Write as.

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.

Chapter 8 Slide the Eraser. Question 1 write the following using exponents? 7 · 7 2 · 2 · 2 x · x · x· x · x· x · x.

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

Opener-NEW SHEET-11/29 Evaluate (1.08) (0.95)25

THE NATURAL BASE EXAMPLE 1 Simplify natural base expressions Simplify the expression. a.e2e2 e5e5 = e = e7e7 b. 12e4e4 3e3e3 = e 4 – 3 4 = 4e4e.

Objective Write and evaluate exponential expressions to model growth and decay situations.

8.1 Exponential Growth p Exponential Function f(x) = b x where the base b is a positive number other than one. Graph f(x) = 2 x Note the end behavior.

Exponential Functions and Their Graphs Digital Lesson.

8.1 Exponential Growth p Exponential Function f(x) = b x where the base b is a positive number other than one. Graph f(x) = 2 x Note the end behavior.

Splash Screen. Then/Now You identified, graphed, and described several parent functions. (Lesson 1-5) Evaluate, analyze, and graph exponential functions.

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.

a≠0, b>0,b≠1, xєR Exponential Growth Exponential Decay (0,a) b > 1, b = _______________ a = __________________ H. Asymptote: y = ______ 0 < b < 1, b =

Exponential Functions Algebra III, Sec. 3.1 Objective Recognize, evaluate, and graph exponential functions.

7.1 Exploring Exponential Models p434. Repeated multiplication can be represented by an exponential function. It has the general form where ***x has D:

Algebra 1 Section 8.5 Apply Exponential Functions When a quantity grows by the same amount each day it is experiencing linear growth. y = mx + b When a.

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

Thurs 2/4 Lesson 7 – 1 Learning Objective: To graph exponential functions & solve interest problems Hw: Pg. 439 #10-25 all.

Graph exponential growth functions. Note: (0,1)

Math II Unit 2 (Part 2). Exponents Exponents EQ: How do you use properties of exponents to simplify algebraic expressions?

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.

Fri 2/5 Lesson 7 – 1 Learning Objective: To graph exponential functions & solve interest problems Hw: Pg. 439 #10, 14, 17 – 22, 26 – 29, CC#45.

8.1 Exponential Growth 8.2 Exponential Decay. Exponential Function An exponential function has a positive base other than 1. The general exponential function.

Do Now: State the domain of the function.. Academy Algebra II 7.1, 7.2: Graph Exponential Growth and Decay Functions HW: p.482 (6, 10, even), p.489.

Graph Y-Intercept =(0,2) Horizontal Asymptote X-Axis (y = 0) Domain: All Real Numbers Range: y > 0.

Algebra 2 Chapter 8 Section 1. Exponential Growth Goal:Graph exponential growth functions. An exponential function involves the expression b x where the.

7-1 Exponential Functions

Exponential Growth and Decay. M & M Lab Part 1- Growth What happened to the number of M&Ms? Part 2-Decay What happened to the number of M&Ms? Increased.

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

HW: pg ,10,14,26-28 Do Now: Take out your pencil, notebook, and calculator. 1) Objectives: You will be able to define exponential functions. You.

Chapter 7 Section 1. EXAMPLE 1 Graph y = b for b > 1 x SOLUTION Make a table of values.STEP 1 STEP 2 Plot the points from the table. Graph y =. x 2.

10.2 Exponential and Logarithmic Functions. Exponential Functions These functions model rapid growth or decay: # of users on the Internet 16 million (1995)

3.1 Exponential Functions. Mastery Objectives Evaluate, analyze, and graph exponential functions. Solve problems involving exponential growth and decay.

Section 11-2 Graphs of Exponential Functions Objective: Students will be able to 1. Graph exponential functions and inequalities 2.Solve real life problems.

Chapter 7 Exponential and Logarithmic Functions. 7-1 Exponential Growth.

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

continuous compound interest

Chapter 5: Inverse, Exponential, and Logarithmic Functions

Do Now: Think about the function y = 2x. What do you think happens when x gets really big and positive? How about when x gets really big and negative?

Section 8.8 – Exponential growth and Decay

Examples Compound Interest

Algebra II H/G Section-07-02

Examples Compound Interest

Determine all of the real zeros of f (x) = 2x 5 – 72x 3 by factoring.

Algebra II H/G Section-07-02

Presentation transcript:

Do Now Rhonda hears a rumor at 8:00 A.M. She immediately tells her two best friends the rumor. One hour later Rhonda’s friends have each told two of their friends. This pattern continues each hour, with each friend reporting the rumor to two friends who have not already heard it. By 8:00 P.M. that evening, how many people have heard the rumor? Answer: 8191

Chapter 8 Section 1 Exponential Growth Mr. Ochoa Algebra II

Vocabulary Exponential Function- Base- Asymptote- Exponential Growth Function- Growth Factor-

Examples Objective - To graph exponential functions and to model them in real-life situations.

Graph

y-intercept =1 asymptote = x-axis domain:all real numbers range:y > 0

Graph

y-intercept =0.25 asymptote = x-axis domain: range:y > 0 all real numbers

Graph

y-intercept =1 asymptote y = -1 domain: range:y > -1 all real numbers

In 2005 the average price of a car was $15,000. If the price increases 8% a year, what will the average price be in 10 years?

You deposit $50,000 in an investment account that pays 6% annual interest. Find the balance after 2 years if the interest is compounded quarterly ? P = 50,000, r = 0.06 n = 4, t = 2