# Unit 3 Day 7. Exponential Growth & Decay

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Unit 3 Day 7 Exponential Growth & Decay 1

2 Warm Up - Zombies SCENARIO 1 A pack of zombies is growing exponentially! After 1 hour, the original zombie infected 5 people, and those 5 zombies went on to infect 5 people, etc. After a zombie bite, it takes 1 hour to infect others. How many newly infected zombies will be created after 4 hours? If possible, draw a diagram, create a table, a graph, and an equation. SCENARIO 2 During this attack, a pack of 4 zombies walked into town last night around midnight. Each zombie infected 3 people total, and those 3 zombies went on to infect 3 people, etc. After a zombie bite, it takes an hour to infect others. Determine the number of newly infected zombies at 6 am this morning. If possible, draw a diagram, create a table, a graph, and an equation. SCENARIO 3 At 9:00 am, the official count of the zombie infestation was Every hour the number of zombies quadruples. Around what time did the first zombie roll into town? 2

3 New Zombies Time New Zombies y 5 x Time (hours) 3

4 New Zombies Time (hours) 4 Time New Zombies y 4(3) x

5 x 7 x 2AM Later in this unit, we ll learn how to solve these problems algebraically. For now, one way to solve is by using the calculator! Do y1 = 16384, y2 = (4) x then find intersection in calc. 5

6 Homework Answers Packet p odds & \$4, 12 p x = 9 3. x = 4 4. No solution 5. x = 4 7. x = 2 9. x = 4 p x = x = a) h 9.8 ft. b) h 10.8 ft. c) h ft. 11. x = 7/2 6

7 Homework: Packet p. 12 & 13 Print Unit 3 Packet and Notes Days

8 Notes Day 7 Exponential Growth and Decay 8

9 What if??? You find a bank that will pay you 3% interest annually, so you consider moving your account, but, your current bank wants to keep you. They offer to compound semiannually! You get 2.5% interest and 1.25% interest at the end of June and 1% interest at the end of December. Which bank is giving you a better deal? We won t actually solve this problem but wouldn t it be nice to know how to in case you ran into a similar situation? Let s learn some about these types of problems today! 9

10 Review of Vocabulary Initial Value: The 1 st term in a sequence or the dependent value associated with an independent value of 0. Looking at Zombie Warm-up #2 During this attack, a pack of 4 zombies walked into town last night around midnight. Each zombie infected 3 people total, and those 3 zombies went on to infect 3 people, etc. Initial Value = 4 Common Ratio: The ratio of one term in a sequence and the previous term. Looking at Zombie Warm-up #2 Common Ratio = 3 Common Difference: The difference between one term in a sequence and the previous term. Looking at the sequence 4, 9, 14, 19, Common Difference = 5 10

11 Review of Vocabulary Recursive Function: a function that can be used to find any term in a sequence if you have the previous term (i.e. NOW-NEXT) Looking at Zombie Warm-up #2 During this attack, a pack of 4 zombies walked into town last night around midnight. Each zombie infected 3 people total, and those 3 zombies went on to infect 3 people, etc. Next = Now * 3 Start = 4 Explicit Function: a function that can be used to find any term in the sequence without having to know the previous term. (i.e. y = or f(x) = ) Looking at Zombie Warm-up #2 y = 4(3) x 11

12 Review of Vocabulary Domain: the set of all input values for a function Looking at Zombie Warm-up #2 y = 4(3) x the domain is all real numbers Theoretical Domain: the set of all input values for a function without consideration for context Looking at Zombie Warm-up #2 y = 4(3) x the theoretical domain is all real numbers Practical Domain: the set of all input values for a function that are reasonable within context Looking at Zombie Warm-up #2 y = 4(3) x the practical domain is x 0 because x is time in hours after 6 AM and it doesn t make sense to think about negative time We ll discuss these terms more later today!! 12

13 Note: Function is decreasing over time Note: Function is increasing over time 13

14 14

15 1 - r b = * r is the common ratio This is because you begin with 100% (1 when written as a decimal) and subtract the same percentage each time. 15

16 16

17 1 + r b = * r is the common ratio This is because you begin with 100% (1 when written as a decimal) and add the same percentage each time. 17

18 Examples 1. A house that costs \$200,000 in 2010 will appreciate in value by 3% each year. a. Write a function that models the cost of the house over time. Use x for years after 2010, and y for the value of the house, in dollars. y b. Find the value of the house in \$ 268, ,000(1.03) x c. In what year will the house value have doubled? Year 2033 More vocab you must know! *Appreciate means increasing rate *Depreciate means decreasing rate 18

19 Examples 2. The most recent virus that is making people ill is a fast multiplying one. On the first day of the illness, only 2 virus bugs are present. Each day after, the amount of bugs triples. a. Write a function that models the bugs growth over time. Let x represent the number of days since the onset of the illness and y represent the amount of bugs. y 2(3) x b. Find the amount of bugs present by the 5 th day. y 5 2(3) 486 bugs 19

20 Examples 3. You have a bad cough and have to attend your little sister s choir concert. You take cough drops that contain 100 mg of menthol in each drop. Every minute, the amount of menthol in your body is cut in half. a. Write a function that models the amount of menthol in your body over time. Let x represent minutes since you took the cough drops and y be the amount of menthol, in mg, remaining in your body. b. It is safe to take a new cough drop when the amount of menthol in your body is less than 5 mg. How long will it be before you can take another cough drop? y 100(1 1 ) 20 About 4.3 minutes 2 x More vocab you must know! *Half Life = Amount of time for a substance to be cut in half For this problem, the half life is 1 minute

21 Example! Let s try a tougher problem you may run in to! 4. You have a bad cough and have to attend your little sister s choir concert. You take cough drops that contain 100 mg of menthol in each drop. Every 5 minutes, the amount of menthol in your body is cut in half. Remember Half Life = Amount of time for a substance to be cut in half a. Write a function that models the amount of menthol in your body over time. Let x represent minutes since you took the cough drops and y be the amount of menthol, in mg, remaining in your body. y = 100(1/2) t/5 you must do t/5 exponent so that the exponent will determine the number of half lives that have occurred b. It is safe to take a new cough drop when the amount of menthol in your body is less than 5 mg. How long will it be before you can take another cough drop? 5 = 100(1/2) t/5 Do y1 = 5, y2 = 100(1/2) t/5 then find intersection in calc. 21

22 In the problems above, we wrote explicit functions for the exponential data. BUT we also need to know how to write recursive functions for the exponential data. Make sure you include the starting value of your data a this will always be where the independent variable is 0. Next = Now * b, Starting at a (You must tell the values of b and a) 22

23 Let s write the prior examples using Recursive Formulas! Next = Now * b, Starting at a 1. A house that costs \$200,000 in 2010 will appreciate in value by 3% each year. Next = Now * 1.03, Start = 200, The most recent virus that is making people ill is a fast multiplying one. On the first day of the illness, only 2 virus bugs are present. Each day after, the amount of bugs triples. Next = Now * 3, Start = 2 3. You have a bad cough and have to attend your little sister s choir concert. You take cough drops that contain 100 mg of menthol in each drop. Every minute, the amount of menthol in your body is cut in half. Next = Now * 0.5, Start =

24 You Try # Tobias ate half a banana in his room and forgot to throw the rest away. That night, two gnats came to visit the banana. Each night after, there were four times as many gnats hanging around the banana. a. Write an explicit function that models the gnats grown over time. Use x for nights after you first see the gnats and y for number of gnats. y 2(4) x b. Tobias mom said that he would be grounded if the gnats number more than 120. On what night will Tobias be in trouble, if he doesn t step in and solve his gnat problem? x 120 2(4), so x 3 c. Write a recursive function to model the gnats growth. Next = Now * 4, Start = 2 24

25 You Try #5 5. JaCorren is 60 inches and going through a growth spurt. For the next year, his growth will increase by 1% each month. Let x represent number of months and y represent JaCorren s height in inches. a. Write an explicit function that models JaCorren s growth spurt over the next year. y 60(1.01) x y 60(1.01) x b. Find JaCorren s height at the end of the year. y 12 60(1.01) in. c. Write a recursive function to model JaCorren s growth. Next = Now * 1.01, Start = 60 25

26 You Try #6 6. Ian s new Mercedes cost him \$75,000 in From the moment he drives it off the lot, it will depreciate by 20% each year for the first five years. a. Write an explicit function that models the car s depreciation. Use x for years after 2014 and y for the car s value, in dollars. y 75000(1.20) x y 75000(.80) x b. What will the car s value be in 2019? y (.80) \$24,576 c. Write a recursive function to model the car s depreciation. Next = Now *.80, Start = 75,000 26

27 More on Theoretical and Practical Domain When you write an equation for a situation and use it to make predictions, you assume that other people who use it will understand the situation as well as you do. That s not always the case when you take away the context, so we sometimes need to provide some additional information to accompany the equation. The domain of a function is the set of all the possible input values that can be used when evaluating it. If you remove your functions from the context of this situation and simply look at the table and/or graph of the function, what numbers are part of the theoretical domain of the function? Will this be the case with all exponential functions? Why or why not? When you consider the context, however, not all of the numbers in the theoretical domain really make sense. We call the numbers in the theoretical domain that make sense in our situation the practical domain. If you look at the tables for the problems, we can find what numbers would be a part of the practical domain. 27

28 More on Theoretical and Practical Domain Let s find the theoretical domain and practical domain of some of the practice problems you just did. Together 4. Tobias ate half a banana in his room and forgot to throw the rest away. That night, two gnats came to visit the banana. Each night after, there were four times as many gnats hanging around the banana. You try 5. JaCorren is 60 inches and going through a growth spurt. For the next year, his growth will increase by 1% each month. Let x represent number of months and y represent JaCorren s height in inches. 28

29 Homework: Packet p. 12 & 13 Print Unit 3 Packet and Notes Days

30 Practice Exponential Word Problems Scavenger Hunt OR Additional Practice 30

### Lesson 14: Modeling Relationships with a Line

Exploratory Activity: Line of Best Fit Revisited 1. Use the link http://illuminations.nctm.org/activity.aspx?id=4186 to explore how the line of best fit changes depending on your data set. A. Enter any

### GRADE 8 BASELINE TEST 2013 MATHEMATICS. 1 Hour 30 Minutes

GRADE 8 BASELINE TEST 2013 GRADE 8 BASELINE TEST MATHEMATICS 2013 MATHEMATICS 1 Hour 30 Minutes 1 Hour 30 Minutes SCHOOL:. LEARNER:.. CLASS: 1 Baseline Assessment Instrument Gr 8 (135 marks) Read the questions

### Monday Tuesday Wednesday Thursday

Name: Weekly Math Homework - Q1:1 Teacher: Monday Tuesday Wednesday Thursday Use Order of Operations to simplify. Use Order of Operations to simplify. Use Order of Operations to simplify. Use Order of

### Height (ft) Find the average rebound percentage for your ball. Show your work.

Different balls bounce at various heights depending on things like the type of ball, the pressure of air in the ball, and the surface on which it is bounced. The rebound percentage of a ball is found by

### 4-3 Rate of Change and Slope. Warm Up. 1. Find the x- and y-intercepts of 2x 5y = 20. Describe the correlation shown by the scatter plot. 2.

Warm Up 1. Find the x- and y-intercepts of 2x 5y = 20. Describe the correlation shown by the scatter plot. 2. Objectives Find rates of change and slopes. Relate a constant rate of change to the slope of

### Height (ft) Find the average rebound percentage for your ball. Show your work.

Different balls bounce at various heights depending on things like the type of ball, the pressure of air in the ball, and the surface on which it is bounced. The rebound percentage of a ball is found by

### STRATEGIES ACHIEVE MATHEMATICS SUCCESS

STAMS SERIES D STRATEGIES TO ACHIEVE MATHEMATICS SUCCESS PROVIDES INSTRUCTIONAL ACTIVITIES FOR 12 MATHEMATICS STRATEGIES USES A STEP-BY-STEP APPROACH TO ACHIEVE MATHEMATICS SUCCESS PREPARES STUDENTS FOR

### PATTERNS & FUNCTIONS

PATTERNS & FUNCTIONS University of Houston Central Campus September 23, 2006 1 Warm-up Activity Test your knowledge by answering the following questions. No calculations or finger counting allowed. Good

### 21 st Century Math Projects

* +, -. + / 0 1. 2 3 4 5 3 6 7 8 /! " # \$ " % & ' ( )! ) If you are reading this, I ve likely become a Zombie. Do not trust that the rules of Zombieland will keep you safe. The Zombies have seen this film

### GCSE Mathematics Practice Tests: Set 5

GCSE Mathematics Practice Tests: Set 5 Paper 2H (Calculator) Time: 1 hour 30 minutes You should have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser,

### CH 34 MORE PYTHAGOREAN THEOREM AND RECTANGLES

CH 34 MORE PYTHAGOREAN THEOREM AND RECTANGLES 317 Recalling The Pythagorean Theorem a 2 + b 2 = c 2 a c 90 b The 90 angle is called the right angle of the right triangle. The other two angles of the right

### Common Core State Standards

0 03 Pacing Guide for Sixth Grade Common Core State Standards Math Content Standards Ratios and Proportional Relationships RP Understand ratio concepts and use ratio reasoning to solve problems. The Number

### 8-1. The Pythagorean Theorem and Its Converse. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary

8-1 he Pythagorean heorem and Its Converse Vocabulary Review 1. Write the square and the positive square root of each number. Number Square Positive Square Root 9 81 3 1 4 1 16 1 2 Vocabulary Builder leg

### Tying Knots. Approximate time: 1-2 days depending on time spent on calculator instructions.

Tying Knots Objective: Students will find a linear model to fit data. Students will compare and interpret different slopes and intercepts in a context. Students will discuss domain and range: as discrete

### Pacific Charter Institute Pacing Guide Grade(s): _5 Subject Area: _Math in Focus grade 5 CP: yes _X no

Week 1 Pre-requisite skills review Chapter 1 pre-test Assessment 5 chapter pre-test pp. 1-4 or MIF Student book 5A pp. 1-4 Reteach 4A (1.1, 1.2, 2.1, 3.2, 3.4) NWEA Kids start Wed. Week 2 1.1 Writing numbers

### Accuplacer Arithmetic Study Guide

Accuplacer Arithmetic Study Guide Section One: Terms Numerator: The number on top of a fraction which tells how many parts you have. Denominator: The number on the bottom of a fraction which tells how

March Madness Basketball Tournament Math Project COMMON Core Aligned Decimals, Fractions, Percents, Probability, Rates, Algebra, Word Problems, and more! To Use: -Print out all the worksheets. -Introduce

### Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question

Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 11, Lesson 1 1. Warm up 2. Notes Review 3. ICA QUIZ 57 Warm up

### MORE TRIGONOMETRY

MORE TRIGONOMETRY 5.1.1 5.1.3 We net introduce two more trigonometric ratios: sine and cosine. Both of them are used with acute angles of right triangles, just as the tangent ratio is. Using the diagram

### THE BEHAVIOR OF GASES

14 THE BEHAVIOR OF GASES SECTION 14.1 PROPERTIES OF GASES (pages 413 417) This section uses kinetic theory to explain the properties of gases. This section also explains how gas pressure is affected by

### 100-Meter Dash Olympic Winning Times: Will Women Be As Fast As Men?

100-Meter Dash Olympic Winning Times: Will Women Be As Fast As Men? The 100 Meter Dash has been an Olympic event since its very establishment in 1896(1928 for women). The reigning 100-meter Olympic champion

### Algebra 3.5 day 1.notebook. September 10, Bellwork

Bellwork 1 Go over Quiz 2 Partners 3 Before we have our HW quiz, check your work and answers with last night's HW with your partner. If there is something your partner is not sure about, help them. If

### MATH 110 Sample 02 Exam 1

1. Evaluate: log 4 64 [A] 3 [B] 1 12 [C] 12 [D] 1 3 2. Given log 5 = T and log 2 = U, find log. [A] T + U [B] TU [C] T + U [D] TU. 3. Find x if e x 52 8 =, and ou are given ln 8 = 2.0794. [A] 0.3999 [B]

### 3. Answer the following questions with your group. How high do you think he was at the top of the stairs? How did you estimate that elevation?

J Hart Interactive Algebra 1 Classwork Exploratory Challenge 1. Watch the first 1:08 minutes of the video below and describe in words the motion of the man. Elevation vs. Time #2 [http://www.mrmeyer.com/graphingstories1/graphingstories2.mov.

### Mathematics (Project Maths Phase 3)

*B6* Pre-Leaving Certificate Examination, 2014 Triailscrúdú na hardteistiméireachta, 2014 Mathematics (Project Maths Phase 3) Paper 1 Ordinary Level 2½ hours 300 marks Name: School: Address: Class: Teacher:

### = ( 3) = positive negative zero positive negative zero

Name Date Period # Adding and subtracting Integers Teaching Point: Add and subtract integers by using a rule Standards: 7.NS.A.1a, b, c, d Adding Integers: Same sign: The sum of two positive integers is

### Name Date Period. E) Lowest score: 67, mean: 104, median: 112, range: 83, IQR: 102, Q1: 46, SD: 17

Chapter 6 Review Standards: 4, 7, 8, and 11 Name Date Period Write complete answers, using complete sentences where necessary. Show your work when possible. MULTIPLE CHOICE. Choose the one alternative

### Bellwork MCT Practice Test (Form A) Problem numbers.

Course 7 th Grade Math Student Objective (Obj. 5d) TSW determine probability through experimentation and calculations. DETAIL LESSON PLAN Tuesday, April 16 / Wednesday, April 17 Lesson 12-1, 12-2 Probability

### ACTIVITY: Finding a Formula Experimentally

8.1 Volumes of Cylinders How can you find the volume of a cylinder? 1 ACTIVITY: Finding a Formula Experimentally Work with a partner. a. Find the area of the face of a coin. b. Find the volume of a stack

### Reliability. Introduction, 163 Quantifying Reliability, 163. Finding the Probability of Functioning When Activated, 163

ste41912_ch04_123-175 3:16:06 01.29pm Page 163 SUPPLEMENT TO CHAPTER 4 Reliability LEARNING OBJECTIVES SUPPLEMENT OUTLINE After completing this supplement, you should be able to: 1 Define reliability.

### Lesson 22: Getting the Job Done Speed, Work, and Measurement Units

Lesson 22: Getting the Job Done Speed, Work, and Measurement Units Student Outcomes Students decontextualize a given speed situation, representing symbolically the quantities involved with the formula.

### Note! In this lab when you measure, round all measurements to the nearest meter!

Distance and Displacement Lab Note! In this lab when you measure, round all measurements to the nearest meter! 1. Place a piece of tape where you will begin your walk outside. This tape marks the origin.

### A Study of Olympic Winning Times

Connecting Algebra 1 to Advanced Placement* Mathematics A Resource and Strategy Guide Updated: 05/15/ A Study of Olympic Winning Times Objective: Students will graph data, determine a line that models

### Year 10 Mathematics, 2007

Student s Name: Teacher s Name: 10 Year 10 athematics, 2007 lgebra Use straightforward algebraic methods and sketch and interpret features of linear graphs Time: 20 minutes. Check that you have entered

### Calculating Forces in the Pulley Mechanical Advantage Systems Used in Rescue Work By Ralphie G. Schwartz, Esq

Calculating Forces in the Pulley Mechanical Advantage Systems Used in Rescue Work By Ralphie G. Schwartz, Esq Introduction If you have not read the companion article: Understanding Mechanical Advantage

### Parametric Ball Toss TEACHER NOTES MATH NSPIRED. Math Objectives. Vocabulary. About the Lesson. TI-Nspire Navigator System

Math Objectives Students will be able to use parametric equations to represent the height of a ball as a function of time as well as the path of a ball that has been thrown straight up. Students will be

### Translations: Comparison Sentences

Translations: Comparison Sentences A comparison sentence is a special form of translation, a single sentence within a word problem that provides information about two different things: two unknowns. In

### here she is viewers she s got positivity plus, it s Saaaally Newsworth!

Percent Equation (is/of = %/100) MA6871 Activity Introduction Welcome to Math News Now! Where we speak the language of numbers. Today s top story, solving percent problems. (pause) And bringing you news

### Title: 4-Way-Stop Wait-Time Prediction Group members (1): David Held

Title: 4-Way-Stop Wait-Time Prediction Group members (1): David Held As part of my research in Sebastian Thrun's autonomous driving team, my goal is to predict the wait-time for a car at a 4-way intersection.

### 1. Determining Solution Concentration

In this exercise you will determine the concentration of salt solutions by measuring samples with known concentration and making a calibration curve. You will review units of concentration, and how to

### CHAPTER 8 (SECTIONS 8.1 AND 8.2) WAVE PROPERTIES, SOUND

Name Period CHAPTER 8 (SECTIONS 8.1 AND 8.2) WAVE PROPERTIES, SOUND 1 ACTIVITY LESSON DESCRIPTION SCORE/POINTS 1. NT NOTES PACKET (notes and study questions ) _ /50 NT NOTES PACKET (vocab definitions &

### NYC Marathon Quarter 1 Review Task. The New York City Marathon was last weekend. Over 50,000 people ran 26.2 miles around the city!

NYC Marathon Quarter 1 Review Task Name: Alg: The New York City Marathon was last weekend. Over 50,000 people ran 26.2 miles around the city! 1. The 2015 male winner was Stanely Biwott, his time was 2

### 4.8 Applications of Polynomials

4.8 Applications of Polynomials The last thing we want to do with polynomials is, of course, apply them to real situations. There are a variety of different applications of polynomials that we can look

### Below are the graphing equivalents of the above constraints.

Detailed Step- by- Step description of the Wilson Problem Part A. LP Formulation Step 1. Figure out the problem Although it may seem obvious, the first step in solving the Wilson Problem is to understand

### The Bruins I.C.E. School

The Bruins I.C.E. School Lesson 1: Addition & Subtraction Word Problems Lesson 2: Extend the Counting Sequence Lesson 3: Extend the Counting Sequence Lesson 4: Understand Place Value Lesson 5: Represent

### Mathematics Spiral Review Quarter 1.1 Grade 5

Mathematics Spiral Review Quarter 1.1 Basic Computation (4.NBT.4) 378 + 1,761 = Write 538 using number names and expanded form. Estimation (4.NBT.3) Round to the nearest hundred: 329 6,582 Skill of the

Library Guide Grade 6 Renaissance Learning P. O. Box 806 Wisconsin Rapids, WI 9-806 Phone: (800) 8-0 FAX: (71) - Email: answers@renlearn.com Support Email: support@renlearn.com Web Site: www.renlearn.com

### STAAR Practice Test #1. 2 (2B) What is the equation in standard form of the line that

STAAR Practice Test #1 TEKS 2 (Linear Equations) 1. (2B) The population of Webb County, Texas, from the year 2000 through 2010 is shown in the graph. If the trend shown in the graph continues, what will

### Pythagorean Theorem in Sports

Name Date Pythagorean Theorem in Sports Activity 1: Pythagorean Theorem in Baseball Directions: Measure the distance between each of the bases using the yard stick provided. Then convert your measurements

### Gears Ratios and Speed / Problem Solving

Teacher Mechanics Note to the teacher On this page, students will learn about the relationship between gear ratio, gear rotational speed, wheel radius, diameter, circumference, revolutions and distance.

### Pre-Algebra Chapter 3 Decimals and Equations

Pre-Algebra Chapter 3 Decimals and Equations SOME NUMBERED QUESTIONS HAVE BEEN INTENTIONALLY DELETED OR REMOVED. YOU WILL NOT BE USING A CALCULATOR FOR PART I MULTIPLE-CHOICE QUESTIONS, AND THEREFORE YOU

### Pressure of the atmosphere varies with elevation and weather conditions. Barometer- device used to measure atmospheric pressure.

Chapter 12 Section 1 Pressure A gas exerts pressure on its surroundings. Blow up a balloon. The gas we are most familiar with is the atmosphere, a mixture of mostly elemental nitrogen and oxygen. Pressure

### Decimals Worksheets. The decimal point separates the whole numbers from the fractional part of a number.

Decimal Place Values The decimal point separates the whole numbers from the fractional part of a number. 8.09 In a whole number the decimal point is all the way to the right, even if it is not shown in

### The Battleship North Carolina s Fire Control

The Battleship North Carolina s Fire Control Objectives: 1. Students will see the application of trigonometry that the Mark 14 gun sight used with the 20mm guns aboard the NC Battleship. (Geometry SCOS:

### Cumulative Test. Name. Score. Show all work on this paper. Please use the Student Reference Guide.

Name Score Math Course 1 1A 1. Use the numbers 6, 12, and 18 to make two addition facts and two subtraction facts. 12 + 12 12 + 12 12 12 12 12 2. Use the numbers 5, 15, and 75 to make two multiplication

### Warm Up Find what numbers the following values are in between.

Warm Up Find what numbers the following values are in between. 1. 30 2. 14 3. 55 4. 48 Color squares on each side of the triangles with map pencils. Remember A square has 4 equal sides! Looking back at

Quadratic Word Problems Normally, the graph is a maximum ( x 2 /opens down) because of the real life scenarios that create parabolas. The equation of the quadratic will be given. We will only be using

### The Application of Temperature and/or Pressure Correction Factors in Gas Measurement

The Application of Temperature and/or Pressure Correction Factors in Gas Measurement COMBINED BOYLE S CHARLES GAS LAWS To convert measured volume at metered pressure and temperature to selling volume at

### Basic organization of the training field

Burke Athletic Club u4 & 5 Training Scheme Phase I Introduction to Soccer 1v1 Legend The purpose of this training program is to allow the u4 and 5 s the opportunity to learn some basic ideas and experience

### Liquid Level Measurement

Technical Article Liquid Level Measurement A pressure transmitter can be used to determine the liquid level in a tank, well, river or other body of liquid. The pressure at the bottom of a liquid filled

### Perimeter. Name. 22 Topic 17. Reteaching Find the perimeter of the figure below.

Perimeter Reteaching 1-1 Find the perimeter of the figure below. 15 m x 4 ft 4 ft 2 ft y 2 ft 5 ft 6 m 20 ft Reteaching 1-1 By using a formula: There are two equal lengths and equal widths, so you can

### Equation 1: F spring = kx. Where F is the force of the spring, k is the spring constant and x is the displacement of the spring. Equation 2: F = mg

1 Introduction Relationship between Spring Constant and Length of Bungee Cord In this experiment, we aimed to model the behavior of the bungee cord that will be used in the Bungee Challenge. Specifically,

### Put in simplest radical form. (No decimals)

Put in simplest radical form. (No decimals) 1. 2. 3. 4. 5. 6. 5 7. 4 8. 6 9. 5 10. 9 11. -3 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 3 28. 1 Geometry Chapter 8 - Right Triangles

### Bikes and Energy. Pre- Lab: The Bike Speedometer. A Bit of History

Bikes and Energy Pre- Lab: The Bike Speedometer A Bit of History In this lab you ll use a bike speedometer to take most of your measurements. The Pre- Lab focuses on the basics of how a bike speedometer

### 3. Answer the following questions with your group. How high do you think he was at the top of the stairs? How did you estimate that elevation?

Classwork Exploratory Challenge 1. Watch the first 1:08 minutes of the video below and describe in words the motion of the man. Elevation vs. Time #2 [http://www.mrmeyer.com/graphingstories1/graphingstories2.mov.

### Name. Dear Mr. Henshaw Reading Vocabulary Study Guide Reading is Fundamental

Name Date Due Grading Sheet! For Teacher Use Only! Criteria Points Possible Points Earned Did the student write his or her name on each page of this Reading Study Guide along with the date that this Reading

### Bouncing Ball A C T I V I T Y 8. Objectives. You ll Need. Name Date

. Name Date A C T I V I T Y 8 Objectives In this activity you will: Create a Height-Time plot for a bouncing ball. Explain how the ball s height changes mathematically from one bounce to the next. You

### Cumulative Test. Name. Score. Show all work on this paper. Please use the Student Reference Guide.

Name Score Math Course 1 1B 1. Use the numbers 5, 11, and 16 to make two addition facts and two subtraction facts. 11 + 12 12 + 12 12 12 12 12 2. Use the numbers 4, 16, and 64 to make two multiplication

### Boyle s law Verifying the relation between air pressure and volume measuring air pressure in a closed container.

Objective The purpose of this activity is to analyze the relationship between the pressure and volume of a confined gas at constant temperature, create a hypothesis and proceed to test it using the Labdisc

### The Ideal Gas Constant

Chem 2115 Experiment # 8 The Ideal Gas Constant OBJECTIVE: This experiment is designed to provide experience in gas handling methods and experimental insight into the relationships between pressure, volume,

### GEOMETRY CIRCLING THE BASES PRE-VISIT - BALLPARK FIGURES - PART 2

PRE-VISIT - BALLPARK FIGURES - PART 2 OBJECTIVE: Students will be able to: Identify the formulas for finding circumference and area of a circle. Calculate the circumference and area of given circles. TIME

### Special Right Triangles

GEOMETRY Special Right Triangles OBJECTIVE #: G.SRT.C.8 OBJECTIVE Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. *(Modeling Standard) BIG IDEA (Why is

### 2008 Excellence in Mathematics Contest Team Project B. School Name: Group Members:

2008 Excellence in Mathematics Contest Team Project B School Name: Group Members: Lassie - TEAM PROJECT B 2008 Excellence in Mathematics Contest The Team Project is a group activity in which the students

### TOPIC III: Proportional Reasoning. Good Luck to:

Good Luck to: Period: Date DIRECTIONS: Show all work in the space provided. 1. Joniqua wants to get an A in her Algebra 1 class. So far she has four test scores; 77%, 83%, 97%, and 95%. Which choice best

### Navigate to the golf data folder and make it your working directory. Load the data by typing

Golf Analysis 1.1 Introduction In a round, golfers have a number of choices to make. For a particular shot, is it better to use the longest club available to try to reach the green, or would it be better

### The Bruins I.C.E. School Math 3 rd 5 th Grade Curriculum Materials

The Bruins I.C.E. School Math 3 rd 5 th Grade Curriculum Materials Lesson 1: Line Plots Lesson 2: Bar Graphs Lesson 3: Mean, Median, Mode, Range, Maximum and Minimum Lesson 4: Classifying Angles Lesson

### Building System Dynamics Models

Building System Dynamics Models Stella Guide 6 Overshoot and Collapse Deer Population Vegetation 7000.00 90000.00 3500.00 45000.00 0.00 0.00 0.00 5.00 0.00 5.00 0.00 Graph p () Years 4:0 pm Mon, Feb 6,

### the tower one at a time as she speaks.], a red here or a red here. So that s

esearcher: Professor Carolyn Maher Page: 1 of 9 1 1 four things taken one at a time to four things taken two at a time. 2 Stephanie Um hm. 3 1 Okay. 4 2 Okay. 5 1 So you were going to ask another question

### Frequency Distributions

Descriptive Statistics Dr. Tom Pierce Department of Psychology Radford University Descriptive statistics comprise a collection of techniques for better understanding what the people in a group look like

### CC Investigation 1: Graphing Proportions

CC Investigation 1: Graphing Proportions DOMAIN: Ratios and Proportional Relationships Problem 1.1 During the first basketball game of the season, Karl made 3 of his 5 free-throw attempts. Karl then made

### Unit 3 Trigonometry. 3.1 Use Trigonometry to Find Lengths

Topic : Goal : Unit 3 Trigonometry trigonometry I can use the primary trig ratios to find the lengths of sides in a right triangle 3.1 Use Trigonometry to Find Lengths In any right triangle, we name the

### Vocabulary: Objectives: Materials: For Each Station: (Have 2 stations for each liquid; 8 stations total, in student groups of 3-4) Students will:

Author: Ms. Adrienne Maribel López Date Created: August 2007 Subject: Properties of Matter Level: 6 th 8 th grade Standards: NYS Learning Standards for Mathematics, Science, and Technology-- Intermediate

### Unit 1 Summary. License Math: Basic Math in Real Estate. Converting fractions to decimals

Converting fractions to decimals Some real estate math problems will contain fractions. While it is possible to solve the problem using fractions, it s typically easier to convert the fraction to a decimal

### Mini-Golf Course Description. 1. You must draw your design on a piece of graph paper so that it will cover all four quadrants.

Algebra 1 Mrs. Blake B256 Mini-Golf Course Description Guidelines for your creation: 1. You must draw your design on a piece of graph paper so that it will cover all four quadrants. 2. On the graph paper

### The Rise in Infield Hits

The Rise in Infield Hits Parker Phillips Harry Simon December 10, 2014 Abstract For the project, we looked at infield hits in major league baseball. Our first question was whether or not infield hits have

### The distance-time graphs below represent the motion of a car. Match the descriptions with the graphs. Explain your answers.

Motion Graphs 6 The distance-time graphs below represent the motion of a car. Match the descriptions with the graphs. Explain your answers. Descriptions: 1. The car is stopped. 2. The car is traveling

### Gabe represents his mystery number with the variable f.

Mystery Numbers Home Link 7- Gabe and Aurelia play Number Squeeze. Gabe represents his mystery number with the variable f. - a. Represent each of the two Number Squeeze clues with an inequality. Describe

### Bet Majestic Introductory Guide to Sports Betting

Bet Majestic Introductory Guide to Sports Betting 1 Introduction Welcome to the Bet Majestic Betting Guide and thank you for becoming a subscriber to our Bet Majestic community. You have joined with many

### No offense There is no offside offense if a player receives the ball directly from: a goal kick a throw-in a corner kick

Understanding FIFA Law 11: Offside One of the most difficult laws of the game to understand and enforce is Offside. There are times during a game when a player can be in an offside position, but not violate

Performance Task # 1 Goal: Arrange integers in order. Role: You are a analyzing a Julie Brown Anderson s dive. Audience: Reader of article. Situation: You are interviewing for a job at a sports magazine.

### How to finish a dart game. Discussion of various out shots, percentage out shots and game ending shots and strategies by Mike Sexton.

How to finish a dart game. Discussion of various out shots, percentage out shots and game ending shots and strategies by Mike Sexton. There has been much discussion in my 35 + years of dart playing about

### Multiple Representations of Buoyancy. Meredith Weglarz, Jessica Oliveira, James Vesenka University of New England, Department of Chemistry and Physics

Multiple Representations of Buoyancy Meredith Weglarz, Jessica Oliveira, James Vesenka University of New England, Department of Chemistry and Physics Abstract: A modeling lab exercise, based on multiple,

### The Pythagorean Theorem Diamond in the Rough

The Pythagorean Theorem SUGGESTED LEARNING STRATEGIES: Shared Reading, Activating Prior Knowledge, Visualization, Interactive Word Wall Cameron is a catcher trying out for the school baseball team. He

### Wednesday 4 November 2015 Morning

Oxford Cambridge and RSA F Wednesday 4 November 2015 Morning GCSE MATHEMATICS A A501/01 Unit A (Foundation Tier) * 5 1 2 2 8 6 9 9 5 9 * Candidates answer on the Question Paper. OCR supplied materials:

### Development of the Coast Guard Commercial Fishing Vessel Checklist Generator. EPSS development and HPT

Development of the Coast Guard Commercial Fishing Vessel Checklist Generator EPSS development and HPT Background: Congress enacted legislation that required all commercial fishing industry vessels that

### HKA TECHNOLOGIES INC. TEMPERATURE COMPENSATION

HKA TECHNOLOGIES INC. TEMPERATURE COMPENSATION Different Methods of Air Leak Testing Conventional vs Bell Jar Pressure Decay and Differential Pressure Decay Mass Flow and Differential Mass Flow HKA mainly

### A school trip. An evening of your favourite television programmes. A rehearsal plan. To cook a two course meal.

Experience & Outcome: MNU 2-10a use and interpret electronic and paper-based timetables and schedules to plan events and activities, and make time calculations as part of my planning. recognise types of

### Averages. October 19, Discussion item: When we talk about an average, what exactly do we mean? When are they useful?

Averages October 19, 2005 Discussion item: When we talk about an average, what exactly do we mean? When are they useful? 1 The Arithmetic Mean When we talk about an average, we can mean different things