In Chapter 2 you looked at multiple representations (such as a table, graph, equation, or situation) of linear functions. In this chapter you will use.

Slides:

Advertisements

Similar presentations

Connection Patterns & Functions.2

Advertisements

ANALYZING SEQUENCES Practice constructing sequences to model real life scenarios.

Real-World Adventures with Representations Quadratic and Exponential functions.

WARM UP Write down objective and homework in agenda.

9-7 Linear, Quadratic, and Exponential Models

Linear Systems The definition of a linear equation given in Chapter 1 can be extended to more variables; any equation of the form for real numbers.

WEEK 3 (23-26 SEPTEMBER 2013) HOMEWORK DUE TUESDAY: “TEXTING BY THE NUMBERS” DUE WEDNESDAY: HOW ARE YOU UNDERSTANDING DATA AND TECHNOLOGY? DUE THURSDAY:

So far in this course, you have been investigating the family of linear functions using multiple representations (especially tables, graphs, and equations).

I. The parent function of a quadratic

Is this relation a function? Explain. {(0, 5), (1, 6), (2, 4), (3, 7)} Draw arrows from the domain values to their range values.

+ Hw: pg 788: 37, 39, 41, Chapter 12: More About Regression Section 12.2b Transforming using Logarithms.

Graphs of Functions Defined by Expressions in a Linear Equation On a standard screen, graph the following functions, determined from the given linear equation:

Section 1.2 Exponential Functions

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.

Many games depend on how a ball bounces. For example, if different basketballs rebounded differently, one basketball would bounce differently off of a.

In Lesson 5.1.2, you found that the relationship between the height from which a ball is dropped and its rebound height is determined by a constant multiplier.

: Unit 3 Lesson 1 Jeopardy: Remediation Activity 2.

7.1.2 What is the connection? Multiple Representations of Exponential Functions.

Slide 1 Lesson 76 Graphing with Rates Chapter 14 Lesson 76 RR.7Understand that multiplication by rates and ratios can be used to transform an input into.

Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Recursive Routines Exponential Equations Multiplying with Exponents.

In Lessons and 4.1.3, you investigated connections between tile patterns, x → y tables, graphs, and rules (equations). Today you will use your observations.

Bell Work Copy the Diamond Problems below onto your paper. Then use the pattern you discovered to complete each one.

In the bouncing ball activity from Lessons and 5. 1

Look at the tables and graphs below. The data show three ways you have learned that variable quantities can be related. The relationships shown are linear,

For each rule make a table, graph, and draw figure 0, 1, and 2.

Lesson – Teacher Notes Standard:

How can you see growth in the rule?

Lesson – Teacher Notes Standard: 8.F.A.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically.

In Chapter 3, you studied different ways to represent patterns. You organized information into tables, graphed information about patterns, and learned.

What is the graph about? Is it linear? AMSTI-Bouncing Balls.

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.

 Class Introduction: Exponential Growth So far in this course, you have been investigation the family of linear functions using multiple representations.

What do you think of when you hear the word “exponential?”

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,

Name the next number in the sequence: a) 1, 3, 9, 27, … b) 1, 5, 25, 125, …

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

2.1.1 Calling Plans day 4 calling cards Unit 2: Linear Relationships SWBAT: Compare calling plans by using graphs, tables, and equations.

9-7 Linear, Quadratic, and Exponential Models. Linear, Quadratic, & Exponential Review.

Polynomials Properties Functions Find xDefinitions

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%

LINEAR VS. EXPONENTIAL FUNCTIONS & INTERSECTIONS OF GRAPHS.

Linear Vs. Non-Linear Functions We are learning to model functions as tables, graphs and equations (rules). Monday, June 27, 2016.

Objectives: 1. Look for a pattern 2. Write an equation given a solution 4-8 Writing Equations from Patterns.

Lesson – Teacher Notes Standard:

Let’s Get Ready To Play Some Let’s Get Ready To Play Some . . .

Chapter 1 Linear Equations and Graphs

Example Use the bar graph to answer the following questions. Approximate the number of endangered species that are birds. Find the bar labeled birds.

Chapter 1 Linear Equations and Graphs

A Real Life Problem Exponential Growth

5.OA 1-3 Test Prep.

How can I express this situation efficiently?

RELATIONS AND FUNCTIONS

7. The tuition at a private college can be modeled by the equation ,

5.OA 1-3 Test Prep.

E-4. 4: Constant Ratios in the context of Real-world Situations E-4

Lesson – Teacher Notes Standard:

Exponential Functions

The inequalities you have seen so far are simple inequalities

Multiplying Like Bunnies

Bell Work Cronnelly Span of tightrope: 19 feet

4.3 Recursion and Exponential Functions

Linear, Exponential, or Neither

Lesson – Teacher Notes Standard:

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.

Lesson – Teacher Notes Standard:

3 Chapter Chapter 2 Graphing.

Arithmetic, geometric, or neither

In this lesson, you will learn to write an exponential growth function modeling a percent of increase situation by interpreting the percent of increase.

Lesson / – How Does it Grow

Presentation transcript:

In Chapter 2 you looked at multiple representations (such as a table, graph, equation, or situation) of linear functions. In this chapter you will use multiple representations to learn more about the multiplier and starting point of exponential functions. In Chapter 2 you looked at multiple representations (such as a table, graph, equation, or situation) of linear functions. In this chapter you will use multiple representations to learn more about the multiplier and starting point of exponential functions.

7-20. Let’s look at some of the connections between the multiple representations of an exponential function. a.) Arnold dropped a ball during the bouncing ball activity and recorded its height in a table. Part of his table is shown at right. What was the rebound ratio of his ball? At what height did he drop the ball? Write an equation that represents his data. Explain your equation. b.) A major technology company, ExpoGrow, is growing incredibly fast. The latest prospectus (a report on the company) said that so far, the number of employees, y, could be found with the equation y = 3(4) x, where x represents the number of years since the company was founded. How many people founded the company? How can the growth of this company be described?

c.) A computer virus is affecting the technology center in such a way that each day, a certain portion of virus-free computers is infected. The number of virus-free computers is recorded in the table at right. How many computers are in the technology center? What portion of virus-free computers is infected each day? How many computers will remain virus-free at the end of the third day? Justify your answer. d.) As part of a major scandal, it was discovered that several statements in the prospectus for ExpoGrow in part (b) were false. If the company actually had five founders and doubles in size each year, what equation should it have printed in its report?

7-21. Most of the exponential equations you have used in this chapter have been in the form y = ab x. a)What does a represent in this equation? What does b represent? b)How can you identify a by looking at a table? How can you find it in a situation? Give an example for each representation. c)How can you determine b in each representation? Use arrows or colors to add your ideas about b to the examples you created in part (b).

7-22. MULTIPLE-REPRESENTATIONS WEB What connections are you sure you can use in an exponential functions web? For example, if you have an exponential equation, such as y = 20(3) x, can you complete a table? If so, draw an arrow from the equation and point at the table, as shown at right.

7-23. EQUATION → GRAPH How can you sketch the graph of an exponential function directly from its equation without making a table first? Discuss this with your team. Then make a reasonable sketch of the graph of y = 7(2) x on your paper.