AGENDA Work on Warm Up (5 minutes) Go Over Warm Up (7 minutes) Hurricane Fran and Regression Scenario (15

minutes) In Class Group Project: Real Life Regression (55

minutes) Project assignments and expectations (5 minutes) Work on group project (30 minutes) Presentations (20 minutes)

Closing/Recap/Announcements (8 minutes)

WARM UP1. Solve the following equations:log3(2x + 5) + log33 = log345 3log 7x = 9

2. A new Web site launched in January. It initially got 125 hits. Three months later, it got 2000 hits.

a. Use this information to find r, the continuous growth rate of the number of hits. (hint: N = N0ert )

b. How many hits will it have in November (11 months after it launched)?

3. Sketch the graph of an exponential function. On a separate graph, sketch the graph of a logarithmic function.

4. What does it mean to find the regression of a set of data? What do you do?

TODAY’S OBJECTIVE: USE EXPONENTIAL AND LOGARITHMIC REGRESSION TO GENERATE EQUATIONS THAT MODEL REAL LIFE DATA AND USE THOSE EQUATIONS TO ANALYZE THE DATA AND MAKE PREDICTIONS.

NC Standards Addressed:

Create and use calculator-generated models of linear,

polynomial, exponential, trigonometric, power, and logarithmic

functions of bivariate data to solve problems.

a) Interpret the constants, coefficients, and bases in the context of the data.

b) Check models for goodness-of-fit; use the most appropriate model to draw conclusions and make predictions.

HURRICANE FRAN

Hurricane Fran slammed into North Carolina's southern coast on September 5th, 1996 with sustained winds of approximately 115 MPH, and gusts as high as 125 MPH. At some point, 1.7 million customers in North Carolina and 400,000 customers in Virginia lost electricity. The overall death toll was 37, including 24 in North Carolina. Flooding was also a severe problem in North Carolina, Virginia, West Virginia, and Maryland. Fran produced rainfall amounts of over 10 inches in parts of eastern North Carolina and western Virginia.

DAMAGESDamages for homes and

businesses in North Carolina were estimated at approximately $2.3 billion. Damages/costs related to public property (debris removal, roads and bridges, public buildings, utilities, etc) were estimated at about $1.1 billion for NC. Agricultural damage (crops, livestock, buildings) in NC was over $700 million. Wake County (Raleigh and vicinity) alone reported over $900 million in damage to residential and commercial property. Finally, forestry/timber losses for the state probably exceeded $1 billion.

YOUR TASK

Determine which type of equation will generate the best algebraic model of the data, and use that equation to analyze the data and make predictions.

Date Customers without power

Sept 6 1,159,000Sept. 7 804,000Sept. 8 515,000Sept. 9 340,500

Sept. 10 195,200Sept. 11 136,300Sept. 12 77,000Sept. 13 37,600

Date Customers without power

Sept 6 1,159,000Sept. 7 804,000Sept. 8 515,000Sept. 9 340,500

Sept. 10 195,200Sept. 11 136,300Sept. 12 77,000Sept. 13 37,600

LOOKING AT THE SAME SCENARIO FROM A DIFFERENT PERSPECTIVE

Customers without power

Date

1,159,000 Sept 6804,000 Sept. 7515,000 Sept. 8340,500 Sept. 9195,200 Sept. 10136,300 Sept. 1177,000 Sept. 1237,600 Sept. 13

1. Compare this set of data to the data we just looked at. What changed?

X = ________________________________

Y = _______________________________

2. Based on that change, what type of equation is most likely to generate a good algebraic model of the hurricane recovery?

LOOKING AT THE SAME SCENARIO FROM A DIFFERENT PERSPECTIVE

Customers without power

Date

1,159,000 Sept 6804,000 Sept. 7515,000 Sept. 8340,500 Sept. 9195,200 Sept. 10136,300 Sept. 1177,000 Sept. 1237,600 Sept. 13

3. Enter the new data set into your calculator. What window would be appropriate for this data:

X Min:

X Max:

Y Min:

Y Max: 4. Make sure your Stat Plot is still on and look at your graph. Does the equation we picked above match the shape of your scatterplot?

5. Find the type of regression you want and use it to generate your regression equation:

 __________________________________________________

6. Is it a good fit? How do you know?

7. If the recovery continued at the same pace, how long until all power was restored (less than 1,000 customers without power)?

  I would find this answer by:__________________

GROUP PROJECT: MODEL A REAL LIFE DATA SET USING REGRESSION

I will put you into groups of 4 and give each group a scenario with a set of data.

Your Goal: Determine the best equation to serve as an algebraic model of the data and use it to create a presentation about the situation. Possible equations:

Logarithmic Exponential Quadratic Linear

EXPECTATIONS Your group will work together to create a

poster and short (2 minute) presentation of your data and answers to the questions on your sheet.

You will have 30 minutes to work through your questions and create your poster.

Everyone in your group should be working together and on task the entire time. I will be circulating to answer questions as they arise.

GROUP ROLES

LEADER—Responsible for making sure everyone in the group is on task and working together.

SCRIBE—Responsible for writing everything on the group poster

PRESENTER—Responsible for making the group presentation

FACT CHECKER/TIME KEEPER—Responsible for making sure the group is keeping a good pace to complete the assignment on time and checking all answers for accuracy before they go on the poster.

EVERYONE: Be on task, working cooperatively and asking questions as needed.

YOUR POSTER MUST INCLUDE: Title Table of Data Group Members’ Names Defined Variables (what do x and y

represent) Which type of equation you chose to model

your data Regression Equation Correlation Coefficient and what it means Answers to the specific questions on your

scenario

PRESENTATION TIME!

RECAP How do we choose which equation will give us

the best model for our data?

How are logarithmic and exponential functions related?

How do I choose the best window to view my data on a graph?

Why is modeling with functions helpful in the real world?

When is our next quiz? Test?

HOMEWORK

Presidential Practice Worksheet Come to tutoring if you need to! Study for your formulas quiz tomorrow!

Given the name of the formula, write the formula itself.