Exponential Functions Graphing Functions. Geometric Sequence A geometric sequence has a common ratio. Are these geometric sequences?

Slides:

Advertisements

Similar presentations

Exponential Functions

Advertisements

8-6 Compound Interest and Exponential Growth

Exponential Functions Functions that have the exponent as the variable.

Round Goby….A Big Problem for the Great Lakes

State the domain and range of each function. 3.1 Graphs of Exponential Functions.

Financial Algebra © Cengage/South-Western Slide HISTORICAL AND EXPONENTIAL DEPRECIATION Write, interpret, and graph an exponential depreciation equation.

Models of Exponential and Log Functions Properties of Logarithms Solving Exponential and Log Functions Exponential Growth and Decay

Exponential functions

Chapter 2 Functions and Graphs

Partner practice Chapter 8 Review WHITEBOA RD. Chapter 8 Review DRAW -The basic shape of the graph of a linear equation -The basic shape of the graph.

Exponential Functions Topic 3: Applications of Exponential Functions.

SECTION Growth and Decay. Growth and Decay Model 1) Find the equation for y given.

Review: An exponential function is any function of the form: where a ≠ 0, b ≠ 1, and b > 0. If b > 1, the graph is increasing. If 0 < b < 1, the graph.

Algebra 1 Warm Up 9 April 2012 State the recursive sequence (start?, how is it changing?), then find the next 3 terms. Also find the EQUATION for each.

Do Now Three years ago you bought a Lebron James card for $45. It has appreciated (gone up in value) by 20% each year since then. How much is worth today?

So far in this chapter you have looked at several types of sequences and compared linear and exponential growth patterns in situations, tables, and graphs.

Exponential Functions -An initial amount is repeatedly multiplied by the same positive number Exponential equation – A function of the form y = ab x “a”

DO NOW: YOUR PARENTS HAVE DECIDED TO CHANGE YOUR ALLOWANCE AND YOU MUST DECIDE WHICH PLAN WILL GIVE YOU MORE MONEY NEXT MONTH. PLAN A – ON THE FIRST DAY.

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 Geometric Sequences.

This amount will be more than 1 The base of our exponential function.

Compound Interest 8.2 Part 2. Compound Interest A = final amount P = principal (initial amount) r = annual interest rate (as a decimal) n = number of.

Exponential Functions

Exploring Exponential Functions

2. Write an exponential decay function to model this situation.

Evaluate each expression for the given value of x.

Adapted from If a quantity increases by the same proportion r in each unit of time, then the quantity displays exponential growth and.

Chapter 2 Functions and Graphs Section 5 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.

Xy -21/16 1/ xy -25/4 5/ xy -22/9 2/ xy /3 21/9 xy /2 xy

Graphing Exponentials and Logs

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

8.1-2 – Exponential Functions. Ex. 1 Sketch the graph of y = 2 x. Then state the functions domain & range.

Copyright © 2010 Pearson Education, Inc. All rights reserved Sec

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

State the domain and range of each function Exponential Growth and Decay.

Review: exponential growth and Decay functions. In this lesson, you will review how to write an exponential growth and decay function modeling a percent.

Exponential and Logistic Functions. Quick Review.

Exponential Growth & Decay

Exponential and Logarithmic Functions

How can you create an equation for a decreasing geometric sequence? For example, if your car depreciates in value at an exponential rate, how do you know.

Notes Over 5.1 Graphing Exponential Functions Graph both functions on the same graph. xy xy A larger base makes it increase faster.

Review of Chapter 8. Graphing Exponential Functions: Make and table and graph the function for the domain {0, 1, 2, 3} Plug in 0, 1, 2, and 3 in for x.

Do Now  Clickulators.. 60 Frankie took four tests and got an average score of 87.5%. If his fifth test raised his average to 90%, what was his.

$100 $200 $300 $400 $500 $200 $300 $400 $500 Exponents Scientific Notation Exponential Growth and Decay Properties of exponents Geometry Sequences.

SECTION 4.3 EXPONENTIAL FUNCTIONS EXPONENTIAL FUNCTIONS.

5.2 Exponential Functions and Graphs. Graphing Calculator Exploration Graph in your calculator and sketch in your notebook: a) b) c) d)

Representing Exponential Growth. * 2-1. In the book Of Mice and Men by John Steinbeck, two good friends named Bert and Ernie dream of raisin rabbits and.

Exponential Functions Exponential Growth Exponential Decay y x.

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.

DO NOW HW: Exponential Functions Worksheet

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

You have been looking at geometric patterns and ways in which those patterns can be represented with x→y tables, graphs, and equations. In Lesson 4.1.2,

To explore exponential growth and decay To discover the connection between recursive and exponential forms of geometric sequences.

Holt Algebra Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20) and (20,

Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20) and (20, 24). The population of a town is decreasing at a rate of 1.8%

Drill If a quantity increases by the same proportion r in each unit of time, then the quantity displays exponential growth and can be modeled by the.

Graphs of Exponential Functions. Exponential Function Where base (b), b > 0, b  1, and x is any real number.

Obj: Evaluate and graph exponential functions. Use compound formulas. Warm up 1.Find the limit. x ,00050,000100,000150,000 y.

CHAPTER 5 LESSON 5 Exponential Functions and Investing.

E-5. 3: General Form of the Exponential Function E-5

Warm-up 1. Corey bought 48 roses for his girlfriend for Valentine’s Day. Everyday 10% of the roses start to wilt. Write an equation describing this situation.

8.7 Exponential Decay Functions

Arithmetic, geometric, or neither

Exponential Functions

Notes Over 8.6 Exponential Decay

Geometric Sequences and Series

Lesson / – How Does it Grow

Presentation transcript:

Exponential Functions Graphing Functions

Geometric Sequence A geometric sequence has a common ratio. Are these geometric sequences?

Page 116 #29 x1234… Y3579… x1234… Y361224…

Page 116 #29 x1357… Y3… x1357… Y35813…

Page 117 #29 X2468… y3-5-9… X1257… Y1

Page 117 #29 X25811… y … X2534 y2-7-4 X021 Y

Exponential Function Characteristics Exponential functions model Geometric sequences. In a growth graph the pattern shows that the y values increase slowly at first as x increases and then it grows rapidly as x gets larger. In a decay graph the pattern shows that the y values decreases slowly at first as x increases and then it decays rapidly as x gets larger.

Graphs Xy

Graphing xy

Which is growing faster? xy xy

Which graph is steeper? Do these graphs show growth or decay? What point do these graphs have in common(Focal Point)? As x gets smaller what happens to y?

Which is steeper? Do these graphs show growth or decay? What point do these graphs have in common(Focal Point)? As x gets very large what happens to y?

Conclusion about Growth and Decay functions In the function If b>1, the function will show growth. In the function If 0<b<1, the function will show decay

Conclusions about common points All functions of the form have a common point at (0,1)

Focus B Simplest exponential function

Writing exponential functions On Jan 1 Donnie borrowed a dollar from his brother, Mike, who charged him 5% interest compounded daily. The function describing the amount of money he owes,y, in terms of days,x,is

Table XY ……  What is the common ratio?  What is the connection between the base of the equation and the interest rate.

Connecting the situation to the equation If Donnie had borrowed $100 instead of $1, what would the equation be? If Mike had charged him 7% interest on his $100 loan, what would the equation be?

Page 118 #30 like this Leo buys a minivan for $ The vehicle depreciates by 15% each year. Set up a table of values to show the van’s value for the first four years. What is the common ratio? x01234 y

Writing an exponential function If Bradford bought a rare stamp for $800. It appreciates 5% per year. What exponential function represents the value,y, of the stamp after x years?