UNIT 7: EXPONENTIAL AND LOGARITHMIC FUNCTIONS

LESSON 1 DAY 1 – 02/22/16 HONORS: 02/09/16 MULTIPLE REPRESENTATIONS OF EXPONENTIAL FUNCTIONS OBJECTIVE: SWBAT TRANSLATE EXPONENTIAL FUNCTION EQUATIONS, GRAPHS, AND TABLES

Warmup

Review of Linear/Quadratic Functions Think: What do you know about linear functions? Quadratic functions? On the back board, create a word-web that involves anything and everything that you remember about linear and quadratic functions. Think outside the box! Things to think about: How do you describe them? What do their graphs look like? What is the “Standard” or “Normal” equation that we use to represent them? What kinds of real world problems use these types of functions?

Linear and Quadratic Models – How Quickly does Medicine take effect? LinearQuadratic Notes: Graph These Tables! Are there equations you can use to represent these data tables? HoursCells Affected HoursCells Affected

Exponential Functions On a half sheet of paper, perform the same analysis and pattern recognition that we just did with Linear and Quadratic Functions. 1. What is the pattern in the table? 2. How many cells are affected in hour 7? 3. Make a graph of this data table. Extra: What is the equation we can use to represent this table? HoursCells Affected

Questions from the weekend’s HW?

Homework Read and Complete Pre-Lab for M&M Experiment tomorrow

LESSON 1 DAY 2 – 02/23/16 HONORS - 02/11/16 MULTIPLE REPRESENTATIONS OF EXPONENTIAL FUNCTIONS OBJECTIVE: SWBAT TRANSLATE EXPONENTIAL FUNCTION EQUATIONS, GRAPHS, AND TABLES

Questions about the Lab?

M&M Exponential Growth/Decay Lab You can find and use helpful information on pages in your textbooks. DO NOT EAT THE M&M’S UNTIL YOU HAVE FINISHED ALL THE WAY THROUGH QUESTION #13! You will receive a “0” if you do not follow this rule.

Finish your M&M Experiments On to experiment #2! Finish through question #13, where you graph your results. When you are finished, you may eat your M&M’s once you have checked in with Mr. Speer.

Homework due Tuesday Complete M&M Lab Analysis Sheet Completely – ALL Problems filled in and Questions Answered!

LESSON 1 DAY 3 – 03/01/16 HONORS - 02/12/16 MULTIPLE REPRESENTATIONS OF EXPONENTIAL FUNCTIONS OBJECTIVE: SWBAT TRANSLATE EXPONENTIAL FUNCTION EQUATIONS, GRAPHS, AND TABLES

HW Questions?

Exponential Growth vs. Exponential Decay

Cards Game You will receive a pack of cards in different colors Each color represents a different problem to solve There will be one group leader who reads the “Problem Statement” card. All other group members will receive one card each. Rules: You may NOT look at anyone else’s card The group leader may NOT write any notes down The three non-leaders may take notes on the information that is discussed and work out a solution with the leader. When you are prepared, ask the referee for assistance. You may NOT move on to the next color of cards until you are cleared by the referee. DO NOT write on the cards.

Homework Textbook pages #27-29 All, #32, #46-49 All, page 447 #16-21 All BIG QUIZ MONDAY on Complex Numbers – Try Practice Quiz as many times as it takes to yield the correct solutions!

LESSON 1 DAY 4 – 03/03/16 HONORS - 02/15/16 MULTIPLE REPRESENTATIONS OF EXPONENTIAL FUNCTIONS OBJECTIVE: SWBAT TRANSLATE EXPONENTIAL FUNCTION EQUATIONS, GRAPHS, AND TABLES

HONORS only - Quiz Time! Clear your desks! When finished, turn your quiz into the tray and pick up a Sudoku puzzle.

Warmup – Exploration – 15 minutes

What does the equation of an exponential function do to its graph? Vertical Stretch FactorParent BaseHorizontal ShiftVertical Shift (y-intercept of parent) (rate of inc/dec) (y-int shifted) [ horizontal asymptote, y-int shifted ] (0,a) (h,a) [ y=k, (h,a+k) ] XY

What does the equation of an exponential function do to its graph? Vertical Stretch FactorParent BaseHorizontal ShiftVertical Shift (y-intercept of parent) (rate of inc/dec) (y-int shifted) [ horizontal asymptote, y-int shifted ] (0,a) (h,a) [ y=k, (h,a+k) ] XY

Assessment Follow the instructions and analyze the two situations on this sheet as an assessment of your learning on Multiple Representations of Exponential Functions.

Homework Exponential Growth and Decay Assessment sheet – all parts, both sides.

LESSON 2 DAY 1 – 03/04/16 HONORS - 02/16/16 USING LOGARITHMIC FUNCTIONS OBJECTIVE: SWBAT SIMPLIFY LOGARITHMIC EXPRESSIONS AND GRAPH LOGARITHMIC FUNCTIONS

Cards Game You will receive a pack of cards in different colors Each color represents a different problem to solve There will be one group leader who reads the “Problem Statement” card. All other group members will receive one card each. Rules: You may NOT look at anyone else’s card The group leader may NOT write any notes down The three non-leaders may take notes on the information that is discussed and work out a solution with the leader. When you are prepared, ask the referee for assistance. You may NOT move on to the next color of cards until you are cleared by the referee. DO NOT write on the cards.

Homework Finish Exponential Growth and Decay Assessment – all parts, both sides Textbook page 456 #12-31 All

LESSON 2 DAY 2 – 03/07/16 HONORS - 02/18/16 USING LOGARITHMIC FUNCTIONS OBJECTIVE: SWBAT SIMPLIFY LOGARITHMIC EXPRESSIONS AND GRAPH LOGARITHMIC FUNCTIONS

Don’t Forget Turn in your Test Corrections Analysis Guide Cover Sheet along with your original test – no corrections are necessary IF you came to meet with me during the time that you scheduled yourself for. The Test Corrections Guide will be a grade in your gradebook! Turn it in by tomorrow with no penalty – I will assume you were using it to correct your test and review. Many people took advantage of the test corrections! Great job to those who came!

Warmup

How do we solve an exponential equation for x?

The existence of an inverse function of exponentials

Logarithmic Form vs. Exponential Form

Converting from Log to Exp, vice-versa

Evaluating a Logarithm

Let’s try some more!

Homework Finish Exponential Growth and Decay Assessment – all parts, both sides Textbook page 456 #12-31 All – switching from logarithmic form to exponential form and vice-versa

LESSON 2 DAY 3 – 03/08/16 HONORS - 02/19/16 USING LOGARITHMIC FUNCTIONS OBJECTIVE: SWBAT SIMPLIFY LOGARITHMIC EXPRESSIONS AND GRAPH LOGARITHMIC FUNCTIONS

Graphing Exponentials and Logarithms X Y X Y X1248 Y

Gallery Graphs With a partner, you will graph two functions given to you by Mr. Speer. Be conscious of the scale of your axes! You will put a table of values and a graph on your poster paper along with your names. After 10 minutes, you will hang your poster on the wall. When you walk around, you should check the table of values for accuracy AND make a general observation about how the graphs are related. You will have 2 minutes at each graph.

Observations about exponential and logarithmic graphs Logarithmic EquationExponential Equation

Inverse Functions

Exit Ticket

Homework Textbook pages #40-43, #46- 53, #59-70 ALL – These will prepare you for the Quiz on Monday! Quiz on Monday on Exponential Functions and Graphing Growth/Decay, Switching from Log to Exp form, and finding the inverse of a Logarithmic Function

LESSON 3 DAY 1 – 03/10/16 HONORS - 02/22/16 THE NATURAL LOGARITHM AND COMMON LOGARITHM OBJECTIVE: SWBAT USE THE NATURAL LOGARITHM AND COMMON LOGARITHM TO SIMPLIFY EXPRESSIONS AND SOLVE EQUATIONS

HW Questions

Quiz Time! Clear your desks! Keep your HW in the basket underneath your desk.

Observations about exponential and logarithmic graphs Logarithmic EquationExponential Equation

Inverse Functions

Earthquakes!

The Richter Scale How does the Richter scale work? It measures the amplitude (height) of the seismic waves that rock the earth. Level 1 Magnitude – Amplitude of 1 Level 2 Magnitude – Amplitude of 10 Level 3 Magnitude – Amplitude of 100 This trend continues with each level as 10 times stronger than the previous.

The Common Logarithm

Logarithms with special bases Richter Level Amplitude of Seismic Waves , , ,000 61,000, ,000, ,000,000 91,000,000, ?

Richter Scale

Homework Complete the Logarithm Properties Worksheet (All Problems)

Performance Task for Exponential Functions Your Homework for the Rodeo Break is to make a poster/presentation for one of the problems in the textbook. Options for your problem: page #31, 32 (suppose you have $3,000 in the account), 36, 37, 40, 41, 43 What to do: 1. Solve your problem based on the question in the textbook. 2. Each problem involves the use of an exponential growth/decay equation in some way. You are to represent your problem using each of the four mathematical representations: Verbal, Graphical, Numerical, and Algebraic (Symbolic) 3. Create a problem that is asking the same ideas as your problem and write the equation that goes along with your created problem. 4. Prepare a 2 minute presentation (individual) that summarizes your problem, your representations, and your created problem (to be given on Thursday, March 3 rd )

Homework Work on your Performance Task (Due Friday, March 4 th ) Prepare your Presentation (Due Friday, March 4 th )

Warmup